## Department of Physics

### Faculty

Robert H. Austin William Bialek, also Lewis-Sigler Institute for Integrative Genomics Frank P. Calaprice Curtis G. Callan Jr. Edward J. Groth III Steven S. Gubser F. Duncan Haldane William Happer M. Zahid Hasan David A. Huse Igor R. Klebanov Elliott H. Lieb, also Mathematics Daniel R. Marlow Kirk T. McDonald Peter D. Meyers Chiara R. Nappi James D. Olsen Nai-Phuan Ong Lyman A. Page Jr. Alexander M. Polyakov Frans Pretorius Michael V. Romalis |
Associate ProfessorCristiano GalbiatiJason R. Petta Joshua W. Shaevitz, also Lewis-Sigler Institute for Integrative Genomics
Assistant Professor Waseem S. Bakr
Bogdan A. BernevigSimone Giombi Thomas Gregor, also Lewis-Sigler Institute for Integrative Genomics William C. Jones Mariangela Lisanti
Silviu Pufu
Roberto Car, Chemistry Garnet Kin-Lic Chan, Chemistry Mansour Shayegan, Electrical Engineering Yakov G. Sinai, Mathematics David N. Spergel, Astrophysical Sciences David W. Tank, Molecular Biology, Princeton Neuroscience Institute Salvatore Torquato, Chemistry Ned S. Wingreen, Molecular Biology |

### Requirements

Graduate study in the Department of Physics is strongly focused on research. Only the Doctor of Philosophy (Ph.D.) program is offered, for which both beginning and advanced students are accepted (please note that advanced students must still take the general examination). The physics department maintains an active research program with equal emphasis on theoretical and experimental studies. Besides its traditional strengths in theoretical and experimental elementary particle physics, theoretical and experimental gravity and cosmology, experimental nuclear and atomic physics, mathematical physics and theoretical condensed matter physics, it has newer strong and growing groups in experimental condensed matter physics and biophysics.

Students are encouraged to involve themselves in research activities right from the beginning, even while they are still studying basic physics. Early research participation leads to a more mature appreciation of the formal aspects of graduate study. It also allows a closer association with faculty members and a more natural transition to independent research later on. The research for the doctoral dissertation is by far the most important part of the program and should prepare students well for careers in research and teaching at universities, or in research at government or industrial laboratories. The duration of the graduate program is five years, and some students complete the Ph.D. even in a shorter period.

**Interdepartmental Research Opportunities
**In addition to the main program of the department leading to the Ph.D. in physics, there are several interdepartmental programs. An advanced degree in mathematical physics may be obtained through a program of work in the departments of physics and mathematics. Normally, the mathematical physics student is required to pass the general examination in physics. When appropriate, an examination on mathematical topics may be substituted for parts of this examination (see the entry for Mathematics).

Physics department faculty and graduate students are active in research collaborations with scientists in several other departments, including astrophysical sciences (which includes plasma physics), chemical engineering, chemistry, electrical engineering and molecular biology. If prior approval is obtained, students may conduct their research under the supervision of advisers from outside the physics department.

Many of the condensed matter and biophysics faculty in the department are also members of the Princeton Institute for the Science and Technology of Materials (PRISM), located in Bowen Hall. The institute provides excellent opportunities for graduate students to work on collaborative projects with students and faculty from other departments in science and engineering, and contains special modern facilities for materials research. Recent examples of such research projects are the physics of block copolymers, high-temperature superconductors and colloidal crystals. For more information, please see the PRISM listing. The department also cooperates with the School of Engineering and Applied Science in solid-state science studies.

Students whose main interest is plasma physics should consider applying to the Department of Astrophysical Sciences (plasma physics section).

**Physics Colloquia
**Weekly talks are given by local or visiting scientists on research of current interest. The level of these talks is intended for nonspecialists.

**Research Seminars
**Informal research seminars are organized each year by the various research groups in order to exchange information and ideas arising from research work in progress at Princeton and elsewhere. Discussions are led by faculty, visiting physicists and advanced graduate students. The largest of these seminars are the following:

- Seminar in Nuclear Physics
- Seminar in High-Energy Physics
- Seminar on Cosmology
- Seminar in Condensed-Matter Physics
- Seminar in Mathematical Physics
- Seminar in High-Energy Particle Theory (given jointly with the Institute for Advanced Study)

**General Examination
**The general examination covers all major fields of physics, both theoretical and experimental, and places particular emphasis on topics of current interest. To assist in measuring progress, students take a preliminary examination covering the subjects of electromagnetism, elementary quantum mechanics, mechanics, statistical physics and thermodynamics in January or May of the first year.

The advanced part of the general examination covers general relativity; condensed matter; atomic, high-energy and nuclear physics; and biophysics. The student will need to pass a set of required core courses on these topics by the end of his or her second year. Another part of the general examination is the experimental project, a report on an experiment that the student has either performed, or assisted others in performing, at Princeton. The preliminary examination, the experimental project and the core courses requirements constitute the general examination, and they all need to be completed by the end of the second year. The physics department is very eager to get students positioned for a rapid start on their thesis research. Hence, during their second year, students are expected to begin actively working under the supervision of a faculty member on a pre-thesis project, a written report on a topic in the field of interest of the student to be defended by the fall of the third year.

**Research and Dissertation
**After passing the general examination, a student engages in independent, original research in experimental and/or theoretical physics and presents a dissertation describing the work. The final public oral examination of this dissertation is the final requirement for the Ph.D.

**Main Fields of Research**

**Atomic Physics:** The program in atomic physics involves work with simple atomic and molecular systems in the gas phase, at surfaces and in solids. The inherent precision of measurements on simple atomic and molecular systems is used in studies of fundamental physics as well as for certain applications. Experimental work frequently involves the use of Nd:YAG lasers, dye lasers, diode lasers, Ti:sapphire lasers, argon and krypton ion lasers, optical, ultraviolet and infrared spectrometers, microwave and radiofrequency spectrometers, signal processing equipment and computers and their interfacing to apparatus. Students often need a detailed theoretical understanding of certain aspects of quantum mechanics, group theory, electricity and magnetism, nuclear physics, surface physics, physical chemistry, fluid dynamics and plasma physics to complete their dissertation work.

**Biophysics:** From observing the dynamics of single biological molecules to building theories for the neural networks that make possible our perception of the world, there are myriad challenges for physicists and biologists willing to explore the boundary between their disciplines. We believe that the opportunities extend far beyond the application of known physical principles and experimental techniques to biological systems: biology offers us examples of very special physical systems, in which the state of the system represents information that has meaning to the organism and the dynamics of the system implements an “algorithm for living” that embodies functions essential for survival in a complex, fluctuating environment.

**Condensed Matter Experiment:** Condensed matter physics and biophysics may be described as the search for simple, unifying explanations for complicated phenomena observed in liquids and solids. Advances in the field lead to universal concepts that govern the behavior of a large number of particles. Modern research embraces both “quantum” systems (the behavior of electrons in solids at low temperature) and “soft” condensed matter (liquid crystals, polymers and biological structure are examples).

At Princeton, experimentalists are active in topological phases, novel superconductivity in organic metals, spin-liquids, quantum spin-textures, topological insulators, quantum magnetism in spin-chain materials, the physics of nanometer-scale structures, high-temperature superconductors, ferromagnetic oxides, charge and spin density wave compounds, mesoscopic properties of subnanometer wires, quantum control of single electron spins, quantum computing, the fractional quantum Hall effect and topological quantum Hall effect and spin-textures.

**Condensed Matter Theory:** The theoretical condensed matter group is involved in research in four main areas: quantum many-body theory of systems involving strong correlations and/or disorder, statistical mechanics, biological systems and systems far from equilibrium.

**Cosmology Experiment:** Work in cosmology, in close collaboration with the theoretical group, includes analyses of relatively nearby structures from published data and deep surveys of galaxies using the Hubble Space Telescope and ground-based telescopes. The group is on the cutting edge of measurements of the 2.73 K cosmic background radiation (CMB). The CMB is the after-glow of the hot early stages of expansion of our universe; in its temperature and angular distribution are encoded the histories of ionization and structure formation and of the time-evolution of the rate of expansion of the universe.

**Cosmology and Gravity Theory:** Working closely with the experimental group, we use astrophysical, particle physics and superstring theory combined with observations to study gravitation and the origin and evolution of our universe.

The study of the nature of large-scale structure was pioneered in this group two decades ago, and we continue to make leading contributions to theories of the origin of this structure. Crucial elements in the work include the measurements by the experimental group of the 2.73 K thermal background radiation, deep observations of galaxies and the Sloan Digital Sky Survey that operates out of the neighboring Department of Astrophysical Sciences. Cosmic Triangle Plot: current knowledge constraints on the key parameters that define the state of the universe. One of the principle areas of research is the theoretical analysis of the cosmic microwave background, large-scale structure and the expansion of the universe to test and constrain cosmological models and measure cosmological parameters.

The origin of the physical universe and the cosmological model that describes its evolution must ultimately be explained by fundamental physics. Our group also studies the relationship between particle superstring physics and theories of the very early universe, dark matter, the cosmological constant and quintessence.

**High Energy Experiment:** The goal of high energy physics is the understanding of the elementary particles that are the fundamental constituents of matter. The fabulous success of the Standard Model has given us a framework for interpretation of most particle interactions, but it has also created a foundation from which we can begin to explore a deeper level of issues such as the origin of mass, the preponderance of matter over antimatter in the universe, the identity of “dark matter,” the physics of the Big Bang and the microscopic structure of space-time.

**High Energy Theory:** The research effort of the high energy theory group covers a wide range of fields, including quantum field theory, string theory, quantum gravity models in various dimensions, the theory of turbulence, particle cosmology, phenomenology of the Standard Model and beyond, and also computer simulations of problems that arise in these areas.

Members of the high energy theory group are also involved in cross-disciplinary research, applying field theoretic techniques to a variety of problems, including turbulent flow, dissipative quantum systems, the quantum Hall effect and heavy-ion collisions, to name a few.

** ****Mathematical Physics:** The mathematical physics group is concerned with problems in statistical mechanics, atomic and molecular physics, quantum field theory and, in general, with the mathematical foundations of theoretical physics. This includes such subjects as quantum mechanics (both nonrelativistic and relativistic), atomic and molecular physics, disorder effects in condensed matter, the existence and properties of the phases of model ferromagnets, the stability of matter, the theory of symmetry and symmetry breaking in quantum field theory (both in general and in concrete models) and mathematical developments in functional analysis, algebra and modern probability theory, to which such subjects lead.

**Particle and Nuclear Astrophysics:** The particle and nuclear astrophysics program addresses questions of fundamental physics in astrophysical systems. Current research topics include solar neutrinos, WIMP dark matter searches, neutrino-less double beta decay and detection of ultra-high energy neutrinos.

### Courses

**Physics**

**PHY 501 Electricity and Magnetism**

Staff

**PHY 502 Electricity and Magnetism**

Kirk T. McDonald

**PHY 505 Quantum Mechanics I**

Edward J. Groth

**PHY 506 Quantum Mechanics II**

Elliott H. Lieb

**PHY 507 Quantum Mechanics II**

Staff

**PHY 508 Quantum Mechanics II**

Leonardo Rastelli

**PHY 509 Relativistic Quantum Theory (Introduction to Quantum Field Theory)**

Alexander M. Polyakov

**PHY 510 Relativistic Quantum Theory II**

Herman L. Verlinde

**PHY 511 Thermodynamics, Kinetic Theory and Statistical Mechanics**

Frederick D. Haldane

**PHY 521/MAT 585 Mathematical Physics**

Michael Aizenman

**PHY 523 Introduction to Relativity**

Frans Pretorius

**PHY 525 Introduction to Condensed Matter Physics**

Ali Yazdani

**PHY 526 Introduction to Condensed Matter Physics**

Frederick D. Haldane

**PHY 527 Introduction to Nuclear Physics**

Frank P. Calaprice

**PHY 529 Introduction to High-Energy Physics**

Christopher G. Tully

**PHY 531 Selected Topics in Mathematical Physics**

Stephen L. Adler

**PHY 532 Selected Topics in Mathematical Physics**

Bruno L. Nachtergaele

**PHY 533 Relativity**

Alexander M. Polyakov

**PHY 534 Relativity**

Larus Thorlacius

**PHY 535 Condensed Matter/Many-Body Physics**

Staff

**PHY 536 Condensed Matter/Many-Body Physics**

Bogdan A. Bernevig

**PHY 537 Nuclear Physics**

Staff

**PHY 538 Nuclear Physics**

Robert P. Redwine

**PHY 539 Selected Topics in High-Energy Physics**

Igor R. Klebanov

**PHY 540 Selected Topics in Theoretical High-Energy Physics**

Alexander M. Polyakov

**PHY 542 Beyond the Standard Model**

Steven S. Gubser, Christopher G. Tully

**PHY 552 Selected Topics in Theoretical Physics**

Lisa Randall

**PHY 553 Selected Topics in Theoretical Physics**

Kirk T. McDonald

**PHY 554 Selected Topics in Experimental Physics**

Albert J. Libchaber

**PHY 555 Atomic and Molecular Physics**

Elliott H. Lieb

**PHY 556 Modern Optics**

Robert H. Austin

**PHY 557 Electronic Methods in Experimental Physics**

Christopher G. Tully, Norman C. Jarosik

**PHY 558 Methods of Experimental Physics**

Val L. Fitch

**PHY 561 Biophysics**

Staff

**PHY 562 Biophysics**

William Bialek

**PHY 563 Physics of the Universe**

Paul J. Steinhardt

**PHY 564/AST 524 Physics of the Universe**

Paul J. Steinhardt, David N. Spergel

**PHY 567/ELE 567 Advanced Solid-State Electron Physics**

Ravindra N. Bhatt

**PHY 570/MOL 515 Method and Logic in Quantitative Biology**

Ned S. Wingreen, David Botstein

**PHY 580 Extramural Summer Research Project**

Chiara R. Nappi