princeton phd theoretical physics

Graduate School

Astrophysical Sciences

General information, program offerings:, director of graduate studies:, graduate program administrator:.

The Department of Astrophysical Sciences offers advanced training in astrophysics. The faculty and staff in the department conduct world-leading research in theoretical and computational astrophysics, observational astronomy, astronomical surveys, and instrumentation (both hardware and software). The fascinating discoveries of modern astronomy challenge the human understanding of the broadest possible range of physical phenomena. The graduate program in Astrophysical Sciences prepares students for scientific careers in astrophysics through a combination of classes and early and active participation in research projects, culminating in original thesis research. 

The program length is five years. The first two years of the program are dedicated to taking core astrophysics courses and working on up to four semester-long research projects with different faculty members. After the general exam at the end of the second year, students are admitted to candidacy, select a thesis advisor, and work on their thesis research for the remaining three years. 

Under the department’s aegis, an extensive graduate research program in fundamental plasma physics is also conducted at the renowned Princeton Plasma Physics Laboratory (PPPL), located on Princeton’s Forrestal Campus. Please see the  Program in Plasma Physics  page for information about applying for this program. Students interested in fundamental plasma physics and its laboratory and technology applications should apply to the Program in Plasma Physics. Students interested in astrophysical applications of plasma physics (including high-energy astrophysics) should apply to the graduate program in Astrophysical Sciences. 

Program Offerings

Program offering: ph.d..

Before standing for the general examination, students must complete four core astrophysics courses (Stellar Structure, Stellar Dynamics, Interstellar Medium, and Cosmology & Extragalactic Astronomy).  Students have the option to complete additional courses in astrophysics (such as High-Energy Astrophysics, Computational Methods, or Plasma Astrophysics), physics, mathematics, statistics, machine learning, and computation. Students may select additional courses with assistance and approval from the faculty.

Additional pre-generals requirements

Seminar Requirement Graduate students must attend the graduate student seminar every semester, except for their last semester at Princeton. Generally, students take turns giving presentations on various aspects of a field selected by the faculty instructor. The dual purposes are to learn about a topic not covered in the required courses (such as an emerging research field) and gain experience giving presentations. Occasionally, the seminar has a different format, such as a workshop or half-semester modules on various topics.

General exam

At the end of the second year, students take the oral general examination. For the examination, the student chooses four topics out of the following six: dynamics of stellar and planetary systems, cosmology and extragalactic astronomy, stellar structure, high-energy astrophysics, interstellar medium, and plasma astrophysics. These topics are covered by classes offered in the department. A committee of four faculty members tests the student for approximately two hours, primarily about the four chosen subjects and other topics in astrophysics.

Qualifying for the M.A.

The Master of Arts (M.A.) degree is normally an incidental degree on the way to full Ph.D. candidacy. It is earned after a student successfully completes two of the three following requirements: (1) successful completion of the four core courses and any additional courses mapped out by the DGS and/or the adviser; (2) successful completion of the general examination; and (3) production of at least one paper suitable for submission to a journal as part of a departmental research project. The research supervisor must approve the paper. The M.A. may also be awarded to students who, for various reasons, leave the Ph.D. program, provided that these requirements have been met.

Students are required to serve as assistants in instruction for one semester sometime during their graduate career.  The DGS may lift this requirement for students who secure certain competitive fellowships that do not allow teaching.

Dissertation and FPO

The Ph.D. is awarded after the candidate’s doctoral dissertation has been accepted, and the final public oral examination sustained.

• Michael A. Strauss

Associate Chair

• Joshua N. Winn (acting)

Director of Graduate Studies

• Joshua N. Winn

Director of Undergraduate Studies

• Neta A. Bahcall
• Gáspár Áron Bakos
• Amitava Bhattacharjee
• Adam S. Burrows
• Christopher F. Chyba
• Steven C. Cowley
• Bruce T. Draine
• Nathaniel J. Fisch
• Robert J. Goldston
• John J. Goodman
• Jenny E. Greene
• David J. McComas
• Eve C. Ostriker
• Felix I. Parra Diaz
• Eliot Quataert
• Anatoly Spitkovsky
• Romain Teyssier

Associate Professor

• Matthew W. Kunz

Assistant Professor

• Alexandra Amon
• Peter M. Melchior

Associated Faculty

• Mariangela Lisanti, Physics
• Lyman A. Page, Physics
• Frans Pretorius, Physics
• Suzanne T. Staggs, Physics
• Paul J. Steinhardt, Physics
• Robert J. Vanderbei, Oper Res and Financial Eng

Lecturer with Rank of Professor

• Samuel A. Cohen
• Ilya Y. Dodin
• Gregory W. Hammett
• Richard P. Majeski
• Allan H. Reiman
• William M. Tang
• Philip C. Efthimion
• William R. Fox
• Yevgeny Raitses
• Jamie S. Rankin

Visiting Lecturer with Rank of Professor

• Matias Zaldarriaga

Visiting Lecturer

• Michael D. Lemonick

For a full list of faculty members and fellows please visit the department or program website.

Permanent Courses

Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students.

APC 503 - Analytical Techniques in Differential Equations (also AST 557)

Apc 523 - numerical algorithms for scientific computing (also ast 523/cse 523/mae 507), apc 524 - software engineering for scientific computing (also ast 506/cse 524/mae 506), ast 513 - dynamics of stellar and planetary systems, ast 514 - structure of the stars, ast 517 - diffuse matter in space, ast 520 - high energy astrophysics, ast 521 - introduction to plasma astrophysics, ast 522 - extragalactic astronomy, ast 541 - seminar in theoretical astrophysics, ast 542 - seminar in observational astrophysics, ast 551 - general plasma physics i (also mae 525), ast 552 - general plasma physics ii, ast 553 - plasma waves and instabilities, ast 554 - irreversible processes in plasmas, ast 555 - fusion plasmas & plasma diagnostics, ast 558 - seminar in plasma physics, ast 559 - turbulence and nonlinear processes in fluids and plasmas (also apc 539), ast 560 - computational methods in plasma physics, ast 562 - laboratory in plasma physics, ast 568 - introduction to classical and neoclassical transport and confinement, mae 522 - applications of quantum mechanics to spectroscopy and lasers (also ast 564), mae 528 - physics of plasma propulsion (also ast 566), sml 505 - modern statistics (also ast 505).

Future Faculty in the Physical Sciences A Postdoctoral Fellowship to Increase Research Excellence and Faculty Diversity

Victor alonso rodriguez.

PhD in Physics 2021, Harvard University

Victor received a PhD in theoretical physics from Harvard University in 2021, and is currently an FFPS postdoctoral fellow at Princeton University. His research focuses on string theory and theoretical high-energy physics. Victor's interests include fundamental aspects of string perturbation theory, conformal field theory, holographic duality, and black hole physics. His recent research has explored a class of non-perturbative effects in string theory mediated by D-instantons that, in many cases, are directly calculable using perturbative techniques. He has also investigated holographic dualities between two-dimensional string theories and matrix models, as a possible window into a non-perturbative description of string theory.

Electrical and Computer Engineering

Applied physics.

New applications of physics can push the boundary of what is possible in electrical and computer engineering, particularly in the areas of materials and devices, both solid-state electronic and optical. Research in applied physics seeks to enable new directions using a combination of theoretical and experimental investigations of novel quantum phenomena, both at a fundamental level, as well as in applications.

These include physics and technology of materials at the nanometer scale, engineered crystal growth, low dimensional materials (natural and engineered) with quantum degrees of freedom exhibiting novel many-body phenomena, new lasers, sensors and optical technologies. Together, these fields provide new paradigms for the discovery of exotic new materials, systems, and physical principles, and lead to advancements in computation and communication, as well as energy conservation and improved health and environment.

Related News

Research Areas

Princeton Center for Theoretical Science

Upcoming PCTS Events

Please Note: PCTS workshops are not open to the general public, but only to active researchers (unless otherwise indicated.)

A ‘joy ride’ of a career: Peebles wins Nobel Prize in Physics for tackling big questions about the universe

Princeton University professor James Peebles, the Albert Einstein Professor of Science, Emeritus, has been awarded a share of the 2019 Nobel Prize in Physics for his theoretical discoveries in physical cosmology. Pictured: Peebles (second from left), who earned his Ph.D. at Princeton in 1962 and taught at the University his whole career, enjoys a standing ovation during a news conference on campus with Herman Verlinde, the Class of 1909 Professor of Physics and chair of the Department of Physics (left), Princeton President Christopher L. Eisgruber (second from right) and Ben Chang, deputy vice president for communications and University spokesperson.

Early in the morning on Tuesday, Oct. 8, Princeton physicist James Peebles got a call from Sweden. His first thought was, “When you receive a phone call that early in the morning, it’s usually something horrible — or it’s this!”

The “this” turned out to be the 2019 Nobel Prize in Physics . Peebles, the Albert Einstein Professor of Science, Emeritus, and professor of physics , emeritus, had won the prize for “theoretical discoveries in physical cosmology.”

Peebles, who came to campus after receiving an early-morning phone call from Sweden announcing his award, takes a phone call from the media in his office in Jadwin Hall.

Peebles, who received his doctorate in physics from Princeton in 1962, shares the prize with Michel Mayor of the University of Geneva and Didier Queloz of the University of Geneva, Switzerland, and the University of Cambridge. The prize amount is 9 million Swedish kroner, or about $908,280, with Peebles receiving half of the award. 

“James Peebles’ insights into physical cosmology,” the Royal Swedish Academy of Sciences said, “have enriched the entire field of research and laid a foundation for the transformation of cosmology over the last 50 years, from speculation to science. His theoretical framework, developed since the mid-1960s, is the basis of our contemporary ideas about the universe.”

James Peebles was awarded the Nobel Prize in Physics Oct. 8, and celebrated with the University community.

Physical cosmology is the branch of physics and astrophysics that deals with the study of the physical origins, evolution and structure of the universe. It’s the branch that asks and tries to answer some of physics’ biggest questions: How did the universe begin? What is it composed of? Will the universe have an end? What is its eventual fate? These are the questions Peebles has grappled with throughout his career at Princeton, from the early 1960s through to his transfer to emeritus status in 2000.

Kip Thorne, a 1965 graduate alumnus in physics who won the 2017 Nobel Prize in Physics and is the Feynman Professor of Theoretical Physics, Emeritus, at the California Institute of Technology, said: “Jim’s Nobel Prize is so wonderfully deserved! When I was a grad student I watched in awe as he scoped out the creation of elements by nuclear burning in our universe’s first three minutes. He was an inspiration to me and has remained so throughout my career.”

Peebles takes questions from the media and students at a news conference held in Richardson Auditorium, as Eisgruber, a 1983 alumnus who majored in physics and took a class with Peebles as an undergraduate, looks on.

Read more comments from Peebles’ fellow physicists in an earlier story.

Peebles was born in 1935 in St. Boniface, near Winnipeg in Manitoba, Canada. He was a curious child who liked tinkering with gadgets and building things. "One of my earliest memories was throwing a tantrum because I wasn't allowed to put together the coffee percolator,” he said. “I loved to take things apart and put them back together. I loved the way things work." 

Peebles, who attended the University of Manitoba for his undergraduate education, is shown here in his 1958 Brown and Gold yearbook.

Peebles carried this curiosity to the University of Manitoba where he received his bachelor’s degree and then in 1958 proceeded to Princeton. It was there, he said, that he fell in love with physics. But his first choice was particle physics — the study of subatomic particles that make up the universe — rather than cosmology. His academic adviser, Robert Dicke, however, had different ideas. Dicke, a physicist who specialized in gravity, persuaded the young graduate student to study gravity physics.

“Gravity operates on the scale of planets and galaxies — it operates on the scale of the universe — so that’s how I got into cosmology,” Peebles said.

When Peebles was asked in a morning interview about how he felt when he learned he’d received the prize, he was candid. “I’ve been working in cosmology since 1964,” he said. “That’s 55 years. I don’t want to be immodest, but it seems logical to give me the award. I’ve been in the subject and seen it grow from a very small science to an immense science and make enormous progress.”

When Peebles began his work in physical cosmology, however, he was one of only a handful of scientists tackling questions of a cosmological nature. Many researchers viewed the field as a dead end.

“When I started working in this subject back in 1964,” he said, “it was easy for me as a postdoc to do original research because there were only a handful of people across the world doing cosmology. After a few conferences I got to know most of them.”

Peebles, shown here in 1990, became an assistant professor at Princeton in 1965, associate professor in 1968 and full professor in 1972. He transferred to emeritus status in 2000.

Today, the field has ballooned as a new generation of researchers have entered the discipline and added their own perspectives. “It’s a very different situation today,” Peebles added. “Sciences evolve.”

Peebles is optimistic and excited about what discoveries the future will bring. “Physics is a rich subject,” he said, “but it is always changing, with many challenges addressed and many challenges opening up.”

Perhaps his most well-known achievement is the theory of cold dark matter, which Peebles initially proposed in 1982, and his pioneering efforts in identifying cosmic background radiation as the remnant of the Big Bang.

“I find it amazing always to consider that nature operates by rules that we can discover,” he said.

Lyman Page Jr. (left), the James S. McDonnell Distinguished University Professor in Physics, congratulates Peebles (right) during a morning celebration in the physics department.

“Jim Peebles is an extraordinary physicist, a man who has thought deeply and clearly about the structure of the universe,” Princeton President Christopher L. Eisgruber said at an afternoon news conference in Richardson Auditorium. “He exemplifies both Princeton’s tradition of brilliant, pathbreaking research in physics, cosmology and gravitation as well as this University’s commitment to put its best scholars in the classroom.”

Herman Verlinde, the Class of 1909 Professor of Physics and chair of the physics department, lauded Peebles for his pioneering work as a theoretical cosmologist “long before it was popular,” and having “laid the foundation for almost all of modern cosmology.”

At a reception for Peebles in Jadwin Hall, students and staff members of the Department of Physics snap photos and greet him with cheers and applause.

Looking out into the auditorium filled with his colleagues, students and the larger University community, Peebles expressed his gratitude in receiving the award and described his career in the sciences as a “joy ride.”

“I don’t know think you can imagine how good this makes me feel,” he said, to an audience that rose in a standing ovation — more than once.

In answering a question from a student about what advice Peebles would have, he said with endearing forthrightness, “My advice is not to aim for prizes or awards. We’re in this for the joy of research, the fascination, the love of science. … I remember being amazed that I could get paid for this.”

Another Princeton physics Nobel laureate in the auditorium, Joseph Taylor, the James S. McDonnell Distinguished University Professor of Physics, Emeritus, noted that Peebles also wrote an influential book about quantum mechanics, and asked if Peebles might develop a theory combining that subject with physical cosmology.

Peebles (left) chats with Duncan Haldane (second from left), professor of physics and the 2016 Nobel laureate in physics, and students (from far right) Kevin Lin, Edward Tian and Bryan To at an afternoon reception for all members of the greater University community in Rockefeller College Common Room.

“What a wonderful challenge for the next generation,” responded Peebles.

“This room is full of people who are on the way to making wonderful discoveries,” he said.

“The universe is capable of surprising us,” he said. “I don’t think there’s a final theory of everything. It’s theories all the way down. We can be very sure that my theory isn’t the final answer. And we can be very sure that as we discover new aspects of the expanding and evolving universe we will be amazed once again. I hope you guys hurry up and make those discoveries.”

Just as his students and colleagues commended Peebles for how much he has taught them, he returned the sentiment. “I have immensely benefited from knowing that when I have to stand up before students, I better know what I’m talking about.”

Peebles (far left) enjoys a celebratory moment with fellow Princeton Nobel laureates Joseph Taylor, the James S. McDonnell Distinguished University Professor of Physics, Emeritus, second from left (1993, physics); Angus Deaton, the Dwight D. Eisenhower Professor of International Affairs, Emeritus, second from right (2015, economics); and Duncan Haldane, professor of physics, far right (2016, physics).

In a reception held in the Rockefeller College Common Room after the news conference, students and faculty expressed their admiration for their teacher and mentor — and the extraordinary atmosphere of being in the Princeton physics department.

Sophie Dvali, a first-year physics graduate student said, “It is especially amazing getting here to Princeton and all of a sudden someone in your department wins the Nobel Prize, and it’s not the first professor in your department to win the prize. We are walking around the department with all of these crazy smart people. It’s overwhelming.”

Songtian Zhang, a sixth-year Ph.D. candidate in physics, said: “I would run into him at the department tea time or he would sit in on conferences. He is one of those people who you see a lot and is so impressive. You get a sense that ‘Woah, he is very smart.’”

Related Stories

Princeton's James Peebles receives Nobel Prize in Physics .

Princeton University professor emeritus and 1962 graduate alumnus James Peebles has been awarded the 2019 Nobel Prize in Physics "for theoretical discoveries in physical cosmology." He shares the prize with Michel Mayor and Didier Queloz.

A good day for great ideas: Princeton's Haldane wins one for theoretical physics .

Princeton University professor F. Duncan Haldane has been awarded the 2016 Nobel Prize in Physics "for theoretical discoveries of topological phase transitions and topological phases of matter."

'This idea took off': MacMillan wins Nobel Prize for opening huge new field in chemistry .

The 2021 Nobel Prize in chemistry honors David MacMillan's pioneering work in organocatalysis.

­­­­­­‘Great fun’: Manabe wins Nobel Prize in physics for modeling climate change .

Princeton climatologist Syukuro “Suki” Manabe, a pioneer in his field, was celebrated for winning the 2021 Nobel Prize in physics.

Kip Thorne lecture caps celebration of Princeton gravitational research .

Two events held April 12 — the 43rd Hamilton Lecture given by Nobel laureate Kip Thorne and a plaque dedicated to Princeton physicist Robert Dicke — highlighted the history of gravitational research at Princeton.

Princeton's F. Duncan Haldane receives Nobel Prize in Physics .

Princeton alumnus Thorne, former postdoc win Nobel Prize in Physics .

Kip Thorne, a Princeton Graduate School alumnus, is one of three recipients of the 2017 Nobel Prize in Physics. Thorne joins Rainer Weiss and Barry Barish in winning the prize “for decisive contributions to the LIGO detector and the observation of gravitational waves.

Prospects in Theoretical Physics 2024

Announcements.

• Please remember to check out of your apartment by 10:00am on Friday, July 19th.  Leave your ID badge in the apartment or bring it to Rubenstein Commons Meeting Room 4
• Luggage drop off begins at 8:00am on Friday, July 19th - Rubenstein Commons Meeting Room 4 only
• Weeks 1 and 2 Poster Presenters - please pick up your posters in Rubenstein Commons Meeting Room 4 or 5 before departing IAS
• List of Poster Session Presenters for July 18th beginning at 1:30pm in Rubenstein Commons Meeting Room 5
• List of Gong Show Presenters for July 16th beginning at 1:30pm in Wolfensohn Hall
• Please check frequently for lecture schedule updates 
• The daily lunch menu can be found here: https://www.ias.edu/dining/lunch . (Lunch includes a dessert, drink, and choice of one of the following: entree or soup or sandwich or salad)
• Dinner service is 5:30-6:30pm.
• Welcome slides (pdf version)

Program Description

From July 8 to 26, 2024 , the Institute for Advanced Study will partner with Princeton University, offering consecutive summer programs focusing on the field of Ultra-Quantum Matter. The Institute’s two-week Prospects in Theoretical Physics (PiTP) Program will be followed by the one-week PCCM Summer School on Condensed Matter Physics

PiTP 2024 : “Ultra-Quantum Matter”   Date: July 8-19, 2024 PiTP is an intensive two-week summer program designed for advanced graduate students and postdoctoral scholars and will cover a broad range of topics in the theory of highly entangled quantum matter.  This subject cuts across traditional subdisciplines of theoretical physics, and the program will feature lectures from experts in condensed matter physics, high energy physics, and quantum information science. PiTP will occur on the Institute’s campus Monday, July 8 through Friday, July 19. Applications Closed 

PCCM 2024: "Quantum Matter, Superconductivity, Topology and Correlations" Date: July 22-26, 2024 The Princeton Summer School will be held Monday, July 22 through Friday, July 26 on the IAS campus. Registration for week 3, including poster presentation information; will open later in April, 2024, due to an overwhelming interest and response to our joint summer program.  Please check periodically for updates.  Thank you for your understanding and support. for PCCM Summer School Only (No application necessary). Additional information (speakers, topics etc.) and a registration form will be posted when available on the PCCM website . 

PiTP Program Details

For housing, travel, and other administrative PiTP information please see the  FAQ page . 

APPLICATION , deadline Monday, April 1, 2024 at 11:59 pm (Eastern Standard Time). If you have not received your PhD, one letter of recommendation from your thesis advisor is required and should be uploaded with this application or at https://forms.ias.edu/form/pitp-reference-upload-form-2024

Partial List of Program Topics

• Anomalies and generalized symmetries and their applications to quantum matter
• Fermi and non-Fermi liquids
• Matrix product states and tensor networks
• Moiré materials
• Non-equilibrium quantum systems
• Topological and related phases of matter including fractons

Organizing Committee

• Michael Hermele ( University of Colorado)
• Biao Lian (Princeton University)
• Nathan Seiberg (The Institute for Advanced Study)
• Leslie Schoop  (Princeton University)
• Ashvin Vishwanath (Harvard University)
• Sanfeng Wu (Princeton University)
• Ali Yazdani (Princeton University)

PiTP Program Lecturers

• Xie Chen (California Institute of Technology)
• Meng Cheng (Yale University)
• Ignacio Cirac (Max Planck Institute of Quantum Optics)
• Eslam Khalaf (Harvard University)
• Vedika Khemani (Stanford University)
• Masaki Oshikawa (University of Tokyo, ISSP)
• Raquel Queiroz (Columbia University)
• Shinsei Ryu (Princeton University)
• Subir Sachdev (Harvard University)
• Shu-Heng Shao (Stony Brook University)
• Dam Thanh Son (University of Chicago)
• Xiao-Gang Wen (MIT)
• Carolyn Zhang (Harvard University)

If you have questions regarding the PiTP program, please send an email to: [email protected] .

Program History

Program Information

Link to Lecture Recordings

Lecture Notes and Slides

Pre-Reading Materials

Participant Directory

General Information

Travel Hints

Visitor FAQ

Campus and Local Maps

How to Connect to WiFi

Princeton Area - Restaurants, Grocery Stores and Grocery Delivery

Princeton Area - Weekend Activities and Local Public Transportation

Getting Help

If you need help or have questions, email  [email protected] .

Stack Exchange Network

Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Q&A for work

Connect and share knowledge within a single location that is structured and easy to search.

Graduate Physics Problems Books

Need to brush up on my late-undergrad and early-grad physics and was wondering if anyone can recommend books or lecture notes (hard copy, or on-line) that also have solutions.

Two that I have come across are:

Princeton Problems in Physics with Solutions - Nathan Newbury

University of Chicago Graduate Problems in Physics with Solutions - Jeremiah A. Cronin

Spacetime Physics - Taylor & Wheeler (favorite book on special relativity; has a lot of problems with solutions at the back; a lot of the problems really enforce the material and discuss paradoxes)

If possible, please also provide a reason why you like the books as opposed to just listing them.

• soft-question
• resource-recommendations
• 1 $\begingroup$ Take it you've thrown away all your old lecture notes, problem sheets and past papers then? They surely would be the best place to start.. I've given the question +1 all-the-same as I would also be interested in others' suggestions. $\endgroup$ –  qftme Commented May 24, 2011 at 16:39
• $\begingroup$ Yes (lol). I unfortunately threw away my notes. $\endgroup$ –  Kamil Sindi Commented May 24, 2011 at 17:26
• 1 $\begingroup$ This post is old, but I want to add my two cents-it matters what you want the material for. If you are just interested in physics then any of the answers below are fine resources. However, if you are practicing for a particular exam, I cant suggest these sorts of resources as the primary study tool since you are just going to spend huge amounts of time on problems that might not have a significant impact on your exam performance. That is, if you are studying for a qualification exam, its in your best interest to completely exhaust all old exams before moving onto resources like ones below. $\endgroup$ –  DJBunk Commented Nov 14, 2012 at 21:04
• $\begingroup$ Roger Blandford & Kip Thorne, Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics. Lecture notes: Ph 136: Applications of classical physics, cns.gatech.edu/PHYS-4421/caltech136/index.html $\endgroup$ –  Qmechanic ♦ Commented Nov 27, 2018 at 12:38

11 Answers 11

(I have a suggestion to make this question a CW.)

General Physics : (Early undergrad and advanced high school)

• Problems in Physics I.E Irodov - (Highly recommended)
• Problems in Physics S S Krotov - (Once again, highly recommended but out of print)
• Physics Olympiad Books - (Haven't read but saw some olympiad problems back in the day)
• Physics by example (like this book a lot, lower undergrad)
• Feynman's Tips on Physics (Exercises to accompany the famous lectures )

General Qualifying exam books: The following books are a part of a series dedicated to the qualifying exams in American Universities and has a large compilation of problems of all levels. Others in the series include Mechanics , Electromagnetism , Quantum Mechanics , Thermodynamics , Optics and Solid State Physics . Unlike other compilation of exercises for qualifiers (such as Princeton or Chicago Problems, or the one mentioned below), they make no excuse for economy and include as many problems from all levels for each subtopic.

Another good book that I read recently for my exam is the two volume series: A Guide to Physics Problems (Part 2 has some relatively easy but interesting problems. I haven't gone through the first part, which is much much more challenging.)

Thinking Like a Physicist: Physics Problems for Undergrads : I love this book because it fosters a real sense of physical understanding, so it's not just mathematics, but actual physical reasoning. Plus, I found the problems challenging and interesting.

Then, there is always the MIT Open Course Ware in Phsyics , which has undergrad and graduate courses with assignments, lecture notes, tests, problems, solutions, etc.

If its qualifying exam questions and problems that you're after, a lot of universities will post examples of past versions online, its just a matter of looking at the department website hard enough.

• $\begingroup$ +1 @Jen: Thanks. If you know any particularly good qualifying exam questions with answers, do you mind posting them? $\endgroup$ –  Kamil Sindi Commented May 24, 2011 at 20:06
• $\begingroup$ It's pretty google-able - the first page of results for "Physics qualifying exams with answers" turn up a number of past exams and solution banks. $\endgroup$ –  Jen Commented May 24, 2011 at 20:19
• $\begingroup$ Also, the GRE subject test in physics is pretty decent for quickly getting up to speed. There are practice tests available: ets.org/gre/subject/about/content/physics $\endgroup$ –  Jen Commented May 24, 2011 at 20:22

Some review/problem set books that I like are:

Solid State Physics: problems and solutions - Laszalo Mihaly and Michael C. Martin

Problems in Quantum Mechanics with Solutions - Gordon Leslie Squires (The reviews are bare bones but I find the questions to be very good at making you think)

Hope this helps. I am interested to see what other people come up with.

"Problem Book on Relativity and Gravitation" - A. Lightman, W. Press, R. Price, S. Teukolsky

The two you have were my favorites.

For completeness, a couple of others, which also have worked solutions:

L.A. Sena, A Collection of Questions and Problems in Physics

Constantinescu, Problems in Quantum Mechanics

There are many problems and solutions sets available for Caltech's comprehensive "Applications of Classical Physics" course here: http://www.pma.caltech.edu/Courses/ph136/yr2008/

It might be worth it to look at some past problems from physics olympiads. In particular:

International Physics Olympiad website http://www.jyu.fi/ipho/ for high-school students, all problems with solutions. Used to be tricky problems, not its more step-by-step, but still challenging and interesting

Moscow City Physics Olympiad http://olympiads.mccme.ru/mfo/ there is a pdf in russian, but I managed to understand almost every single problem with google translator

And of course BAUPC http://liquids.seas.harvard.edu/oleg/competition/ which has few, but (in my opinion) wonderful problems. Some of them are repeated in the classical mechanics book by David Morin ( http://www.amazon.com/Introduction-Classical-Mechanics-Problems-Solutions/dp/0521876222 )

I'll add absolutely great book with problems in analytical mechanics: G.L. Kotkin and V.G. Serbo , "Problems in Classical Mechanics" It is basically a problem-driven approach to learning Landau's first tome.

Also I really like the book: Zhong-Qi Ma and Xiao-Yan Gu , "Problems & Solutions in Group theory for physicists."

Problems and Solutions on Electromagnetism (Major American Universities Ph.D. by Yung-Kuo Lim

Problems and Solutions on Mechanics: Major American Universities Ph.D. by Yung-Kuo Lim

Problems and Solutions on Thermodynamics (Major American Universities Ph.D. by U.S.T. of China Physics Coaching Class and Yung-Kuo Lim

I think the Y K Lim series are the best to follow, especially for last couple week of preparations. These books have all sort of good problems (with solutions) collected from reputed US universities.

You also can dig the internet for various universities solved exams but that is quite time consuming.

Some problem books on quantum field theory:

T.P. Cheng, L.F. Li, "Gauge Theories of Elementary Particle Physics: Problems and Solutions" , Oxford University Press (2000)

V. Radovanovi, "Problem Book in Quantum Field Theory" , Springer (2008).

• D. Atkinson, P.W. Johnson, "Exercises in Quantum Field Theory: A Self-Contained Book of Questions and Answers" , Rinton Press (2003).

More can be found in this page: http://physics.library.wisc.edu/practicebooks.html

One of the best books for IIT mains and advance exams 2013 is Advanced Problems in School Physics Vol-I & II Cengage Learning

• $\begingroup$ Hi Arvind. Welcome to Physics.SE. Whilst this may theoretically answer the question, it would be preferable to include the essential parts of the answer here, and provide the link for reference. $\endgroup$ –  Waffle's Crazy Peanut Commented Feb 10, 2013 at 12:14

Not the answer you're looking for? Browse other questions tagged soft-question resource-recommendations education big-list or ask your own question .

• Featured on Meta
• Announcing a change to the data-dump process
• We've made changes to our Terms of Service & Privacy Policy - July 2024

Hot Network Questions

• Why isn’t this formula used at all?
• Vanishing of principal minors implies upper triangular up to permutation
• Does GDPR's "Legitimate Interest" allow spam?
• Substitute for saltpetre
• Is the "assemble" a transitive or intransitive verb in "The shelves are easy to assemble"?
• "between" two countries
• Why is it inadvisable to apologise for a car accident?
• Expected cards drawn before first ace and king
• Are there any examples of moving Manses?
• Does the throttling profile data for any STS missions exist?
• Series Expansion of logarithm of integral by Landau and Lifshitz in Statistical Physics (First Part)
• Use of circular predictor in GLMM
• An SF story where an orangutan writes a book that is published
• How can I safely cut cultured countertops containing silica?
• Should I drop a semester due to medical reasons
• Child's teddies "being mean" after dark
• Any idea what game this picture is from?
• How to make an operator form of Part[] to use with // (Postfix)
• Counting Occurrences of a Specific 3-Bit Pattern in a Byte Array
• What happens if your flight is cancelled on the last day of your visa; does it vary by country/region?
• Is it safe to keep an outdated credit card?
• Accessing an overridden Greek letter
• Do I have legal grounds against a book by an ex which depicts private details of my life, including some false events, without permission?
• Could Swashplate be replaced with small electric motors?

Princeton Series in Physics 32

The classic account of the structure and evolution of the early universe from Nobel Prize–winning physicist P. J. E. Peebles

The classic introduction to physical cosmology from Nobel Prize–winning physicist P. J. E. Peebles

Recently a symbiotic relationship between particle and nuclear physics has developed, with techniques and ideas from one field fertilizing developments in the other. This work outlines concepts from modern particle physics important to...

Addressing a variety of theoretical cosmological problems, and emphasizing a mathematical approach, this volume nicely complements Peebles' Physical Cosmology (Princeton Series in Physics, 1971). Ryan and Shepley have concentrated on...

This monograph combines a thorough introduction to the mathematical foundations of n-body Schrodinger mechanics with numerous new results. Originally published in 1971.

Some of the articles in this collection give up-to-date accounts of areas in mathematical physics to which Valentine Bargmann made pioneering contributions. The others treat a selection of the most interesting current topics in the...

A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book has developed. In his interpretation, Dr. Everett denies the existence of a separate classical...

Barry Simon's book both summarizes and introduces the remarkable progress in constructive quantum field theory that can be attributed directly to the exploitation of Euclidean methods. During the past two years deep relations on both...

A timely addition to the literature, this volume contains authoritative reviews of three important areas in the physics of elementary particles. Sam B. Treiman, in "Current Algebra and PCAC," reviews the present state of the weak...

In this book, Robert Israel considers classical and quantum lattice systems in terms of equilibrium statistical mechanics. He is especially concerned with the characterization of translation-invariant equilibrium states by a variational...

From the Nobel Prize–winning physicist

Debashish Chowdhury's critical review of more than a thousand papers not only identifies the complexities involved in the theoretical understanding of the real spin glasses but also explains the physical concepts and the mathematical...

About 120 years ago, James Clerk Maxwell introduced his now legendary hypothetical "demon" as a challenge to the integrity of the second law of thermodynamics. Fascination with the demon persisted throughout the development of...

Axiomatic and constructive approaches to quantum field theory first aim to establish it on precise, non-perturbative bases: general axioms and rigorous definition of specific theories respectively. From the viewpoint of particle...

The last decade has seen striking progress in the subject of renormalization in quantum field theory. The old subject of perturbative renormalization has been revived by the use of powerful methods such as multiscale decompositions;...

The forty-nine papers collected here illuminate the meaning of quantum theory as it is disclosed in the measurement process. Together with an introduction and a supplemental annotated bibliography, they discuss issues that make quantum...

Initially published in Moscow in 1950 following the author's death, this book contains the first chapters of a large monograph Krylov planned entitled The foundations of physical statistics," his doctoral thesis on "The processes of...

The physics of extended systems is a topic of great interest for the experimentalist and the theoretician alike. There exists a large literature on this subject in which solutions, bifurcations, fronts, and the dynamical stability of...

The authors present a rigorous treatment of the first principles of the algebraic and analytic core of quantum field theory. Their aim is to correlate modern mathematical theory with the explanation of the observed process of particle...

Current algebra remains our most successful analysis of fundamental particle interactions. This collection of surveys on current algebra and anomalies is a successor volume to Lectures on Current Algebra and Its Applications (Princeton...

How two charismatic, exceptionally talented physicists came to terms with the nuclear weapons they helped to create

This book presents articles written by leading experts surveying several major subfields in Condensed Matter Physics and related sciences. The articles are based on invited talks presented at a recent conference honoring Nobel laureate...

The Dutch scientist Hendrik Kramers (1894-1952) was one of the greatest theoretical physicists of the twentieth century--and one of a mere handful who have made major contributions across the whole field. Physicists know his name from...

The past century has seen fantastic advances in physics, from the discovery of the electron, x-rays, and radioactivity, to the era of incredible solid state devices, computers, quarks and leptons, and the standard model. But what of the...

During the course of this century, gauge invariance has slowly emerged from being an incidental symmetry of electromagnetism to being a fundamental geometrical principle underlying the four known fundamental physical interactions. The...

Einstein's standard and battle-tested geometric theory of gravity--spacetime tells mass how to move and mass tells spacetime how to curve--is expounded in this book by Ignazio Ciufolini and John Wheeler. They give special attention to...

The interpretation of quantum mechanics has been controversial since the introduction of quantum theory in the 1920s. Although the Copenhagen interpretation is commonly accepted, its usual formulation suffers from some serious...

In the 1930s, physics was in a crisis. There appeared to be no way to reconcile the new theory of quantum mechanics with Einstein's theory of relativity. Several approaches had been tried and had failed. In the post-World War II period...

This widely acclaimed introduction to N = 1 supersymmetry and supergravity is aimed at readers familiar with relativistic quantum field theory who wish to learn about the supersymmetry algebra. In this new volume Supersymmetry and...

Like its predecessor, this book by the renowned physicist Sir Rudolf Peierls draws from many diverse fields of theoretical physics to present problems in which the answer differs from what our intuition had led us to expect. In some...

Stochastic mechanics is a description of quantum phenomena in classical probabilistic terms. This work contains a detailed account of the kinematics of diffusion processes, including diffusions on curved manifolds which are necessary...

Problems in theoretical physics often lead to paradoxical answers; yet closer reasoning and a more complete analysis invariably lead to the resolution of the paradox and to a deeper understanding of the physics involved. Drawing...

Stay connected for new books and special offers. Subscribe to receive a welcome discount for your next order. 

• ebook & Audiobook Cart

Office of the Dean of the Faculty

Alexander polyakov.

Alexander “Sasha” Markovich Polyakov, one of the world’s preeminent theoretical physicists and a leading authority on quantum field theory and string theory, transferred to emeritus on July 1, 2023, after thirty-four years on the faculty at Princeton University. His singular creativity and profound ideas have made a lasting mark on elementary particle physics, statistical mechanics, quantum gravity, and other cutting-edge research areas. Sasha is a prominent member of a group of scientists who were educated in the Soviet Union and gained a worldwide reputation while working there, but chose to leave for the West when such a move became possible.

Sasha was born in Moscow in 1945 into an academic family that was deeply affected by both World War II and the Stalinist purges. His special scientific talents were recognized very early, when he was a secondary school student, and brought him into contact with some of the leading Soviet theoretical physicists, including the great Lev Landau. While a student at the Moscow Institute of Physics and Technology (MIPT), Sasha collaborated with his friend Alexander Migdal on a paper that discovered the celebrated Higgs mechanism independently from researchers in the West. This mechanism later turned out to be of profound importance for the construction of the Standard Model of elementary particle physics.

Sasha graduated from MIPT in 1967 and two years later defended his Ph.D. dissertation at the Landau Institute for Theoretical Physics. In 1970, he wrote a seminal paper conjecturing that a statistical system at the point of second order phase transition is not only scale invariant but also has the so-called conformal symmetry. This key idea has continued to guide Sasha’s research for many years, and it has blossomed into a large research area called conformal field theory.

In 1974, Sasha proposed a set of consistency conditions for such theories that goes by the name “conformal bootstrap.” A dozen years ago, this approach was revived by Sasha’s former graduate student Slava Rychkov (a 2002 Princeton Ph.D.), and by now the conformal bootstrap has become an industry practiced by hundreds of researchers.

Sasha has also collaborated with Alexander Belavin and Alexander Zamolodchikov on a powerful application of the conformal bootstrap to two-dimensional systems. Their remarkable paper, which has been very influential for close to forty years, provided a classification and exact solution of an infinite class of conformally invariant models, which generalize the classic Ising model at its second-order phase transition. This paper was also of major importance for a new approach to string quantization, often called the Polyakov string theory. 

In the 1970s and 1980s, Sasha also made major contributions to the theory of quark confinement in quantum chromodynamics, the fundamental description of the strongly interacting particles such as the proton and neutron. He is also regarded for discovering the ’t Hooft-Polyakov monopole solution, which describes a magnetically charged heavy particle that may be present in some extensions of the Standard Model of particle physics. At the time of his emigration from Moscow in 1988, Sasha was the head of the Department of Quantum Field Theory at the Landau Institute and a corresponding member of the Academy of Sciences of the U.S.S.R.

After entering the U.S., Sasha was approached by several top universities with offers of full professorships. He accepted the offer from Princeton University and joined the physics department in September 1989. Also joining the department that year was Sasha’s friend and long-time colleague Migdal. Since 1999, Sasha has been the Joseph Henry Professor of Physics. An avid outdoorsman, Sasha came to appreciate the natural setting of Princeton and its surroundings. The proximity of the Jersey Shore enabled him to pursue another activity he really enjoyed — taking long swims in the ocean — and his talent for swimming is well-known among his colleagues. While on a trip to Corsica to lecture at a summer school, Sasha managed to swim to a small piece of land quite far from the shore. As a result, the students at the school named it the Polyakov Island. 

In the physics department, Sasha is appreciated for his special advanced graduate courses that are based in part on his beautiful monograph Gauge Fields and Strings (Routledge, 1987). Sasha developed his own signature style of lecturing from memory, without any notes, while emphasizing the conceptual foundations and the unity of theoretical physics. His special topics courses have helped educate and inspire several generations of theoretical physicists, including some of the current leaders of the field. Sasha also developed a popular course on fluid dynamics for advanced undergraduates, which had a broad conceptual appeal.

Sasha’s research in the 1990s was initially focused on two-dimensional quantum gravity, which helped provide a definition of certain low-dimensional models of string theory. Later on, he conjectured a modification of this approach to adapt it to his long-standing interest, the problem of quark confinement. This eventually led Sasha to a collaboration with his Princeton colleagues Steven Gubser and Igor Klebanov on a seminal paper connecting string theory with quantum gauge field theory. This 1998 paper, which is one of the three original works laying out the anti-de Sitter/conformal field theory correspondence, has accumulated close to 12,000 citations in Google Scholar, making it one of the most highly cited papers in high-energy physics. More recently, Sasha has been working on novel quantum approaches to cosmology, as well as on the theory of turbulence.

Sasha’s spectacular scientific accomplishments have earned him worldwide acclaim. He is a member of the U.S. National Academy of Sciences, the American Academy of Arts and Sciences, and a Foreign Member of the French Academy of Sciences. His honors include the American Physical Society’s Dannie Heineman Prize and the Lars Onsager Prize, the International Center for Theoretical Physics’ Dirac Medal, the Royal Netherlands Academy of Arts and Sciences’ Lorentz Medal, the Royal Swedish Academy’s Oscar Klein Medal, the Technion Israeli Institute of Technology’s Harvey Prize, and the German Physical Society’s Max Planck Medal.

In 2013, Sasha was awarded the Breakthrough Prize in Fundamental Physics “for his many discoveries in field theory and string theory, including the conformal bootstrap, magnetic monopoles, instantons, confinement/deconfinement, the quantization of strings in noncritical dimensions, gauge/string duality, and many others. His ideas have dominated the scene in these fields during the past decades.”

Sasha Polyakov has exhibited remarkable foresight throughout his scientific career, and we are confident that his work will remain influential and continue to be appreciated for many years to come. We offer Sasha our very best wishes for his retirement, and hope that he will keep in touch and continue sharing his great wisdom and ideas.

Written by members of the Department of Physics faculty.

Princeton Quantum Initiative

Princeton Quantum Colloquium: TBD, Tim Hsieh (Perimeter Institute for Theoretical Physics)

Title: 

Abstract:  

A light lunch will be served in the Bowen Atrium at noon.

Department of Physics

Amy Androwski

As Academic & Administrative Assistant, Amy Androwski provides key support to the varied activities and needs of the faculty, researchers and students in the High Energy Experiment group as well as to the administrators of the Physics Undergraduate and Graduate programs.  Her responsibilities include integral behind-the-scenes work such as problem-solving, navigating and leading others through university structure and processes, partnering with departmental peers, developing relationships with vendors, managing expense reporting and payments and meeting/event planning.

Amy is a people person who values inclusivity, strong relationships and high-quality communication.  She enjoys applying her skills from her HR career to create a meaningful work experience for herself and others.  

Amy is an involved parent, serving as scout leader and backstage manager for The Nutcracker.  She is also a trained yoga instructor and is passionate about music, reading, the Great Outdoors and youth mentorship. 

• Seminars & Events -
• Directions -
• IT Support -
• Search for:
• Catalysis / Synthesis
• Chemical Biology
• Inorganic Chemistry
• Spectroscopy / Physical Chemistry
• Theoretical Chemistry
• Andlinger Center for Energy and the Environment
• Princeton Institute for Computational Science and Engineering
• Princeton Materials Institute
• Princeton Catalysis Initiative
• Research Facilities Overview
• Biophysics Core Facility
• Crystallography
• Merck Catalysis Center
• NMR Facility
• Mass Spectrometry
• Other Spectroscopy
• Small Molecule Screening Center
• Ultrafast Laser Spectroscopy
• Industrial Associates Program
• Libraries & Computing
• Frick Chemistry Laboratory
• Administration & Staff
• Business & Grants Office
• Frick Event Guidelines
• Faculty & Academic Jobs
• Seminars & Events
• Postdocs Overview
• New Postdocs
• Family-Friendly Initiatives
• Graduate Program Overview
• Academic Program
• Campus Life
• Living in Princeton
• Graduate News
• Undergraduate Overview
• Summer Undergrad Research Fellows in Chemistry
• Other Summer Research Opportunities
• Outside Course Approval
• PU Chemical Society
• Our Commitment
• Resources and Reporting
• Visiting Faculty Research Partnership
• Join the Department

Q&A: Postdoc Ben Lienhard inspired at 2024 Lindau Nobel Meeting

Each year since 1951, the Lindau Nobel Laureate Meetings in Germany bring Nobel laureates, industry and science leaders, and selected students from across the globe together for a week of learning and shared enthusiasms.

This year, Princeton Chemistry Postdoctoral Fellow Benjamin Lienhard of the Rabitz Group was among the 600 students invited to attend the physics-themed meeting in July. We asked Lienhard a few questions about the experience.

Q: What did you learn by attending this year’s Lindau Meeting?

I found the discussions on quantum mechanics, its fundamentals, and applications particularly intriguing. I learned about decades-old experiments that have revealed aspects of the classical-to-quantum boundary and the ongoing, century-old discourse in interpreting quantum mechanics. A particular experiment stood out: a classical field attenuated to the level where quantum-ness would be expected still maintained its classical characteristics, suggesting that drawing a clear boundary may be difficult.

Rabitz Group Postdoc Benjamin Lienhard.

Q: Any new directions in physics that you heard about?

From my perspective, the most promising direction highlighted at the meeting is the potential of artificial intelligence (AI), particularly in solving complex physical problems. While the potential of AI was widely acknowledged, many cautioned about the unavoidable biases and emphasized the need for vigilance when using such tools. Consequently, the often-discussed fear that AI could replace scientists was not widely shared.

Q: What was your favorite part of the week-long meeting?

My favorite part was immersing myself fully in physics amidst the beautiful setting of Lindau. Of course, the discussions with peers and Nobel laureates were incredibly inspiring. I aimed to speak with Professor Alain Aspect and Professor Gerardus ‘t Hooft about the foundations of quantum mechanics. I was fortunate to engage with Professor Aspect but missed Professor ‘t Hooft. I also hoped to take a picture with Professor Didier Queloz to share with my brother, Dr. Florian Lienhard, who works for Professor Queloz. Unfortunately, I didn’t run into him.

Princeton’s Duncan Haldane, the Eugene Higgins Professor of Physics and recipient of the 2016 Nobel Prize in Physics, attended the Lindau Nobel Laureate meeting this year.

Q: How can students like yourself benefit from meetings like this one?

The primary benefit for students attending Lindau is the networking opportunities it provides. Additionally, Lindau is a source of inspiration and helps expand students’ knowledge. One of the most common questions, however, revolved around navigating scientific careers. A remark made by Professor Steven Chu of Stanford stuck with me. I’m paraphrasing, but he said something like: if you are the first to look underneath a rock, you can discover new things without much brilliance; discoveries require brilliance if you are the hundredth person to look underneath the rock.

Quantum materials: Theoretical, experimental and computational physicists develop the technology of the future

Binghamton’s graduate program in physics is young but mighty, and home to transformative research.

• share via twitter
• share via linkedin
• share via email

Look at a flat substance on the atomic scale, and you will find a strange new world that bears little resemblance to what you see with the naked eye.

“When you look at an atomic level, a material isn’t perfectly flat with perfect edges,” explained Binghamton University Associate Professor of Physics Pegor Aynajian. “It can be very rough, with atomic terraces that go in different directions, different edges, and defects.”

Aynajian works in a lab that is cleaner and colder than outer space, conditions that allow researchers to study exotic materials known as magnetic topological insulators at the atomic level. Known as quantum materials, they are at the frontier of condensed matter physics and may someday lead the way to technological innovations worthy of science fiction.

Topological materials and superconductors are among the research lines in Binghamton’s physics program, which encompasses theoretical, computational and experimental physics.

The initial graduate program ended in the 1980s and was relaunched in 2010, said Professor Alexey Kolmogorov, who joined the department in 2012. Since its revival, the program has become stronger every year and made U.S. News and World Reports’ best graduate programs rankings in 2023.

Faculty routinely receive research funding from the National Science Foundation, including Kolmogorov, whose work has been funded every year since 2014, and Aynajian, who received a $534,746 NSF grant in July. In the past 10 years, the physics department has secured three NSF CAREER awards and more than five NSF and Department of Energy grants, as well as a Department of Defense Multidisciplinary University Research Initiatives (MURI) grant.

Today, the program has around 45 graduate students and the department continues to hire new faculty members. Alumni have gone on to work at Google and Intel, in national labs and in academia. Physics undergraduates also participate in research and have even co-authored papers, which has led them to some of the best doctoral programs around the country. It’s an impressive record for a young program, faculty acknowledged.

Some Binghamton physicists work in high-tech labs, while others create computer models. Some need never work in a lab at all, and instead deal with mathematical equations.

“Physics is becoming more collaborative; it’s not like the old days, where there was a single person in an office, writing down a theory,” said Associate Professor Wei-Cheng Lee, a condensed matter theorist who frequently works with Aynajian. “Today’s physics research involves many different people with different areas of expertise.”

What is a quantum material?

Quantum materials exhibit qualities that typically aren’t seen in simple materials or at room temperature, such as superconductivity. At the heart of this phenomenon are tiny fundamental particles known as electrons, which surround an atom’s nucleus; all electrons have a negative charge and repel one another. Quantum materials are broadly defined as solids with exotic properties due to novel quantum behaviors of interacting electrons.

“A superconductor is a material in which electrons can be attracted to each other; they form pairs of electrons,” Aynajian explained. “When they do this, something very interesting happens. They become ‘dissipationless’ in that they can go through the material without any loss of energy.”

That loss is typically expressed through heat, whether a smartphone or a data center, he explained. In metals, electrons are free to move around, which is why they can carry electricity under a small voltage. Diamond and glass, however, are insulators: to get electrons to move, you would need to apply enormous voltage from outside the material.

In quantum materials with novel topological qualities, physicists discovered topological insulators about two decades ago. While they contain a normal insulator, their surfaces are conductors such as copper or gold. As a result, electrons can move freely only on the surface. Recently, physicists have found more exotic materials that exhibit even stranger properties: the electrons may only move at the edges of the sample through a single atomic line. In others, electrons may only be available at the corners.

The first such materials were predicted by theorists and then discovered and realized by experimental physicists — the inverse of many discoveries, which usually begin with experiments and are then explained by theorists.

Quantum materials offer unique opportunities for advancing several rapidly evolving fields, including quantum computers and sensors, which are far faster than traditional technology. Think of it this way: The computers we use every day rely on electrical current and a binary code of ones and zeros that manipulates the flow of this current. In quantum reality, an electron can be in two places simultaneously or pass through another substance.

The end result: a quantum computer that can complete certain calculations within minutes or hours that would take 10,000 years in a traditional computer. This concept is known as quantum supremacy, and scientists from diverse fields and various research institutes — even teams at Google, Microsoft and IBM — are actively working toward achieving it. Today, these kinds of computers are the size of a full laboratory, Aynajian pointed out; they also need cold temperatures in the milli-Kelvin range.

“When we talk about quantum computers, quantum bits called qubits are not defined as ones or zeros, as in a classical computer,” Aynajian explained. “They are in a superposition of both states. This allows quantum computers to perform many computations simultaneously.”

The role of modeling and theory

For condensed matter physicists, the holy grail is a superconductor that can operate at room temperature. At present, eligible materials would require enormous pressure, which would make them impractical, Kolmogorov acknowledged.

His work lies at the intersection between physics, materials science and computer science; he and Professor Elena Roxana Margine have combined their separate advanced computational methods to predict materials that could work as next-generation superconductors. One possibility lies with materials based on boron and carbon. In their latest research, Kolmogorov and Margine suggested not only particular materials but also a way these materials could be synthesized.

As a theorist, Lee doesn’t work in a lab or with supercomputers. Instead, he works with the fundamental principles that underlie the discipline — particularly mathematics.

“I’m a theoretical physicist; we use math as a tool,” he said. “At the end of the day, we need to apply the theory to understand something in the real world. Otherwise, it’s not a theory, even if the math is beautiful.”

As he does sometimes in class, Lee held up a red and blue ribbon to explain how topological materials work. Connect it into a loop, and you form one state; twist that ribbon before connecting the ends, and you have another. You can tangle the ribbon and then untangle it, but the fundamental way that it is connected doesn’t change.

These two states cannot continuously transform into one another without breaking the ribbon, which explains—in essence—how electrons could be limited to certain edges and paths in a material that otherwise doesn’t permit their passage. To use purely mental imagery, consider doughnuts and bowls. Both can be considered deformations of a solid sphere, but they are topologically different because doughnuts have a hole, and bowls don’t. In this sense, doughnuts and mugs are topologically equivalent since both have a hole.

“It is really exciting to see this principle of topology could be realized in quantum materials in the real world, and all of these come directly from basic principles of quantum mechanics!” Lee added.

Any of the department’s paths — theory, computational modeling or experiment — may lead to the next great discovery. Every one of these paths is critical to the effort.

“Research at this level cannot be done by a single person,” Aynajian said. “Collaboration between theorists, experimentalists, materials and computational scientists is essential, and there are always many challenges to overcome. But when it finally works, it’s a great discovery.”

Related Stories

Former Caltech Postdoctoral Scholars Drs. Jack Zhang and Mary Luo Support New Theoretical Chemistry Center

A $30 million lead gift endows the Rudolph A. Marcus Center for Theoretical Chemistry in honor of a lifelong mentor and friend.

Dr. Jack Yongfeng Zhang and Dr. Mary Zi-ping Luo's philanthropy advances the Institute's leadership in chemistry and chemical engineering while honoring the legacy of Nobel Laureate Rudolph (Rudy) A. Marcus, the John G. Kirkwood and Arthur A. Noyes Professor of Chemistry. Zhang and Luo's gift pays tribute to the decades of friendship and support provided to the couple by Marcus.

"Thirty-six years ago, I had the privilege of being Rudy's postdoctoral fellow," says Dr. Zhang, president, CEO, chief scientific officer, and co-founder of Amphastar Pharmaceuticals, Inc. "In scientific exploration, he is my mentor. On the road of life, as both a teacher and a friend, Rudy is more like my father. He is a master of theoretical chemistry. He believes that theorists need to be guided by experiments and connect the scattered dots and blanks between theory and experiment. This thought has deeply influenced us in guiding our current complex drug research and strategies."

Dr. Luo was also a Caltech postdoctoral scholar and is COO, chief scientist, and co-founder of Amphastar Pharmaceuticals, Inc. "Rudy shares our unfailing confidence and passion for theoretical chemistry," she says. "We are humbled and honored for this opportunity to assist in establishing the Marcus Center for Theoretical Chemistry at Caltech."

Zhang and Luo chose to focus their giving on people, empowering the Division of Chemistry and Chemical Engineering to attract and support the most talented and driven faculty, postdocs, and students. This gift will ensure the division's continued preeminence by enhancing research and teaching through the following:

• The Tie-Hua Zhang and Su-Hua Li Zhang Graduate Fellowships, named in honor of Zhang's parents;
• The Liang-Neng Luo and Guo-Hua Lou Luo Postdoctoral Fellowship, named in honor of Luo's parents;
• The Jack Yongfeng Zhang and Mary Zi-ping Luo Discretionary Fund;
• The Rudolph A. Marcus Center Instrumentation and Computing Fund; and
• The Rudolph A. Marcus Center Faculty Recruitment Fund.

"Jack and Mary's generous gift speaks powerfully to our highest aspirations," says Caltech President Thomas F. Rosenbaum, the Sonja and William Davidow Presidential Chair and professor of physics. "It highlights the lifelong connections forged among scholars and mentors at the Institute, while opening doors for following generations of students, postdocs, and faculty members at the leading edge of theoretical chemistry research."

Building on a History of Discovery

Drs. Zhang and Luo's gift is timely for the Division of Chemistry and Chemical Engineering, as developments in quantum science and technology are revealing novel avenues of discovery.

Quantum mechanics provides the fundamental theory of molecular behavior. Since its inception in the early 20th century, theoretical chemists at the Institute have led in understanding its implications for chemistry.

• The late Nobel Laureate and Caltech professor Linus Pauling provided the first theory of the chemical bond.
• The late Aron Kuppermann, professor of chemical physics, emeritus, completed the world's first complete three-dimensional quantum-mechanical calculation of a chemical reaction and pioneered the use of supercomputers for predicting the cross sections and rates of chemical reactions.
• William A. Goddard, III (PhD '65), the Charles and Mary Ferkel Professor of Chemistry, Materials Science, and Applied Physics, invented some of the first computational algorithms for molecules.
• Rudy Marcus developed his now-ubiquitous theory of electron transfer.

Now, a second quantum revolution is underway. New means to control the quantum states of atoms and molecules, together with the intellectual merging of quantum mechanics with theoretical information and computer science, has deepened the understanding of quantum mechanics across the physical sciences.

These advances hold the potential to transform chemistry and chemical engineering. They offer the possibility to move beyond a purely qualitative understanding of quantum behavior to precise computational predictions and design of molecular and material properties, new ways to process spectroscopy with unprecedented resolution through quantum sensing, and the control of chemical reactions by quantum computers.

"The Marcus Center will be a vital accelerator of the transformation in chemistry and chemical engineering being brought about by quantum science," says Dennis A. Dougherty, the George Grant Hoag Professor of Chemistry, who served as chair of the Division of Chemistry and Chemical Engineering from 2019–2024 and worked closely with Zhang and Luo on this gift. "Jack and Mary's philanthropy will allow us to retain and recruit the brightest minds in the field, support their research, and fund novel investigations."

From Exams to Ever After

Drs. Zhang and Luo met at Caltech in 1988, but it was not the first time they had crossed paths. Years earlier, China resumed the examination system after the Cultural Revolution. Of the more than two hundred candidates who took the quantum-chemistry entrance examination for graduate schools in one of the test zones, only nine were qualified. Two of those nine were Zhang and Luo, and—they later discovered—they both had taken the exam in the same room at the same time.

Luo was the youngest and only woman admitted in that quantum chemistry session. She began attending Princeton University in 1980, where she earned a PhD in chemistry.

Having been recommended and sponsored by Nobel Laureate and renowned theoretical physicist C. N. Yang, Zhang began graduate studies in chemistry at the State University of New York at Stony Brook. He first met and began to build a close bond with Marcus when the Caltech professor was giving a lecture at nearby Brookhaven National Laboratory. Marcus encouraged Zhang to come to Caltech, and Zhang joined Marcus's lab in 1988 after earning his PhD.

By then, Luo was already at the Institute, working as a theoretical chemistry postdoc with the late Professor Vince McKoy. During this time, she also completed her memoir, A Generation Lost: China Under the Cultural Revolution , which was published in 1990 by Henry Holt & Company.

It was inevitable that the two would meet, and meet they did: in front of the mailboxes on the first floor of Arthur Amos Noyes Laboratory of Chemical Physics. They were married not long after, and Marcus spoke at the reception in place of Zhang's parents, who were unable to attend.

"Jack and Mary are exceptional people," Marcus says. "Their well-earned success is a testament to their curiosity, skillfulness, and perseverance. I have been fortunate to know them for the last 36 years, and am deeply grateful that they have chosen to support Caltech in my honor. Their generosity will facilitate countless generations of students, postdocs, and faculty to solve hard problems and generate novel ideas."

Marcus, Zhang, and Luo have not only remained lifelong friends, but have also continued to work together. Marcus has served on the scientific advisory board of Amphastar Pharmaceuticals.

The Quantum-Science Future

Drs. Zhang and Luo's gift bolsters Caltech's leadership in quantum science and technology. The Institute is home to theorists and experimentalists who are making pathbreaking discoveries in areas ranging from quantum computing and biomedical imaging technologies to innovative detectors for measuring gravitational waves . Scientists at the Institute also are investigating quantum materials with interesting electronic, magnetic, optical, and superconducting properties that cannot be described using classical physics. Caltech recently broke ground on the Dr. Allen and Charlotte Ginsburg Center for Quantum Precision Measurement , which will accelerate the exploration of quantum phenomena across all scales and propel the invention of instruments to measure these phenomena with unprecedented sensitivity.

" It is a particularly exciting time in chemistry and chemical engineering as we work to harness the potential of quantum mechanics to expand our fundamental understanding of chemical and physical systems and develop new quantum technologies," says Caltech Provost David Tirrell, the Ross McCollum-William H. Corcoran Professor of Chemistry and holder of the Carl and Shirley Larson Provostial Chair. "Jack and Mary's exceptional generosity positions the Institute to continue its pioneering contributions in the field."