Physics

35 Sloane Physics Laboratory, 432.3607
M.S., M.Phil., Ph.D.

Chair
Ramamurti Shankar

Director of Graduate Studies
Steven Girvin (35 SPL, 432.3607, graduatephysics@yale.edu)

Professors
Yoram Alhassid, Thomas Appelquist, Charles Bailyn (Astronomy), Charles Baltay, D. Allan Bromley, Richard Casten, Richard Chang (Applied Physics), Michel Devoret (Applied Physics), Paul Fleury (Applied Physics), Moshe Gai (Adjunct), Steven Girvin, Robert Grober (Applied Physics), Martin Gutzwiller (Adjunct), John Harris, Victor Henrich (Applied Physics), Jay Hirshfield (Adjunct), Pierre Hohenberg (Adjunct), Francesco Iachello, Mark Kasevich, Martin Klein, Samuel MacDowell, William Marciano (Adjunct), Simon Mochrie, Vincent Moncrief, Peter Parker, Daniel Prober (Applied Physics), Nicholas Read, Subir Sachdev, Jack Sandweiss, Michael Schmidt, Ramamurti Shankar, Charles Sommerfield, Katepalli Sreenivasan (Mechanical Engineering), A. Douglas Stone (Applied Physics), John Tully (Chemistry), C. Megan Urry, Michael Zeller

Associate Professors
Sean Barrett, Cornelius Beausang, Paolo Coppi (Astronomy), David DeMille, Samson Shatashvili

Assistant Professors
Colin Gay, Gerd Kunde, Reiner Kruecken, Homer Neal, Robert Schoelkopf (Applied Physics), Jeffrey Snyder, Tilo Wettig

Senior Research Scientists
Robert Adair, Satish Dhawan, Vernon Hughes, Richard Majka, Andrew Szymkowiak, N. Victor Zamfir

Lecturers
Stephen Irons, Henry Kasha

Fields of Study
Fields include experimental atomic physics; theoretical and experimental nuclear, particle, condensed-matter physics; astrophysics; and mathematical physics.

Special Admissions Requirements
The prerequisites for work toward a Ph.D. degree in physics include a sound undergraduate training in physics and a good mathematical background. The GRE General Test and the Subject Test in Physics are required.

Special Requirements for the Ph.D. Degree
To complete the course requirements students are expected to take a set of nine term courses. A set of five core courses (Dynamics, Electromagnetic Theory, Quantum Mechanics I and II, and Statistical Mechanics) serves to complete the student's undergraduate training in classical and quantum physics. A set of four advanced courses, including required courses in classical and quantum field theory, provides an introduction to modern physics and research. Prior equivalent course work may reduce the course requirement for individual students. In addition, all students are required to be proficient and familiar with mathematical methods of physics (such as that necessary to master the material covered in the five core courses) and to be proficient and familiar with advanced laboratory techniques. These requirements can be met either by having had sufficiently advanced prior course work or by taking a course offered by the department. All students will also attend a seminar during their first term in order to be introduced to the various research efforts and opportunities at Yale.

Students who have completed their course requirements with satisfactory grades, pass the qualifying examination, and submit an acceptable thesis prospectus are recommended for admission to candidacy. The qualifying examination, normally taken at the beginning of the third term (and no later than the beginning of the fifth term), is a six-hour written examination covering the five core courses and mathematical methods as described above. Students normally submit the dissertation prospectus before the end of the third year of study. Approximately eighteen months after passing the qualifying examination, but no later than the end of the fourth year, students take an oral examination in their chosen field of specialization (the Field Oral Examination).

There is no foreign language requirement. Teaching experience is regarded as an integral part of the graduate training program. All students are expected to serve as teaching fellows during a portion of their first two years of study. Formal association with a dissertation adviser normally begins in the fourth term after the qualifying examination has been passed and required course work has been completed. An adviser from a department other than Physics can be chosen in consultation with the director of graduate studies, provided the dissertation topic is deemed suitable for a physics Ph.D.

Master's Degrees
M.Phil. See Graduate School requirements.

M.S. (en route to the Ph.D.). Students who complete the first-year graduate courses with a satisfactory record (i.e., at least two Honors or four High Passes) qualify for the M.S. degree.

Program materials are available upon request to the Director of Graduate Studies, Department of Physics, Yale University, PO Box 208120, New Haven CT 06520-8120; e-mail, graduatephysics@yale.edu; Web site, www.yale.edu/physics/.

Courses
PHYS 500a, Dynamics. Yoram Alhassid. TTh 10.30–12
Newtonian dynamics and kinematics, Lagrangian dynamics, small oscillations, Hamiltonian dynamics and transformation theory, completely integrable systems, regular and chaotic motion of Hamiltonian systems, mechanics of continuous systems: strings and fluids.

PHYS 502b, Electromagnetic Theory I. Jack Sandweiss. MW 9–10.30
Classical electromagnetic theory including boundary-value problems and applications of Maxwell equations. Macroscopic description of electric and magnetic materials. Wave propagation.

PHYS 504Lb, Modern Physics Measurements. Simon Mochrie and staff.
A laboratory course with experiments in condensed matter, nuclear, and elementary particle physics. Data analysis provides an introduction to computer programming and to the elements of statistics and probability.

PHYS 506a^u, Mathematical Methods of Physics. Tilo Wettig. MW 9–10.30
Survey of mathematical techniques useful in physics. Includes vector and tensor analysis, group theory, complex analysis (residue calculus, method of steepest descent), differential and integral equations (regular singular points, Green's functions), and advanced topics (Grassmann variables, path integrals, supersymmetry).

PHYS 508a, Quantum Mechanics I. Francesco Iachello. MW 10.30–12
The principles of quantum mechanics with application to simple systems. Canonical formalism, solutions of Schrödinger's equation, angular momentum and spin.

PHYS 512b, Statistical Physics I. Yoram Alhassid. TTh 9–10.30
Review of thermodynamics, the fundamental principles of classical and quantum statistical mechanics, canonical and grand canonical ensembles, identical particles, Bose and Fermi statistics, phase-transitions and critical phenomena, renormalization group, irreversible processes, fluctuations.

PHYS 515a, Topics in Modern Physics Research. John Harris. M 2–3
A seminar course intended to provide an introduction to current research in physics and an overview of physics research opportunities at Yale.

[PHYS 522a, Introduction to Atomic Physics.]

PHYS 524a, Introduction to Nuclear Physics. Richard Casten.
Introduction to a wide variety of topics in nuclear structure, nuclear reactions, and nuclear physics at extremes of angular momentum, isospin, energy, and energy density.

PHYS 526a, Introduction to Elementary Particle Physics. Colin Gay. MW 10.30–12
An overview of particle physics including a historical introduction to the standard model, experimental techniques, symmetries, conservation laws, the quark-parton model, and a semiformal treatment of the standard model.

PHYS 538a, Introduction to Relativistic Astrophysics and General Relativity. Vincent Moncrief. MW 9–10.30
Basic concepts of differential geometry (manifolds, metrics, connections, geodesics, curvature); Einstein's equations and their application to cosmology, gravitational waves, black holes, etc.

PHYS 548a^u and 549b^u, Solid State Physics I and II. A. Douglas Stone [F], Simon Mochrie [Sp]. TTh 1–2.15
A two-term sequence covering the principles underlying the electrical, thermal, magnetic, and optical properties of solids, including crystal structures, phonon, energy bands, semiconductors, Fermi surfaces, magnetic resonance, phase transitions, and superconductivity. Also ENAS 850a^u, 851b^u.

PHYS 570b^u, High-Energy Astrophysics. Charles Bailyn. 3 HTBA
A survey of current topics in high-energy astrophysics, including accreting black holes, black holes and neutron stars, relativistic jets, gamma-ray bursts, and ultra-high-energy cosmic rays. The basic physical processes underlying the observed high-energy emission are also covered. Also ASTR 570b^u.

[PHYS 600b, Cosmology.]

PHYS 602a, Classical Field Theory. Jack Sandweiss. TTh 9–10.30
Covariant formulation of electrodynamics, radiation phenomena, and introduction to general relativity.

PHYS 608b, Quantum Mechanics II. Thomas Appelquist. MW 10.30–12
Approximation methods, scattering theory, and the role of symmetries. Relativistic wave equations. Second quantized treatment of identical particles. Elementary introduction to quantized fields.

PHYS 609a, Relativistic Field Theory I. Charles Sommerfield. TTh 10.30–12
The fundamental principles of quantum field theory. Interacting theories and the Feynman graph expansion. Quantum electrodynamics including lowest order processes, one-loop corrections, and the elements of renormalization theory.

PHYS 610b, Many-Body Theory of Solids. A. Douglas Stone. TTh 10.30–12
Solids as many-particle systems. Second quantization. Green's functions, quantum statistical mechanics, linear response theory. Hartree-Fock theory, perturbation theory, Feynman diagrams at finite temperature. Theory of the electron gas, electron-phonon coupling, BCS theory of superconductivity. Also ENAS 852b.

[PHYS 624a, Group Theory.]

[PHYS 628b, Statistical Physics II.]

PHYS 630b, Relativistic Field Theory II. Charles Sommerfield. TTh 9–10.30
An introduction to nonabelian gauge field theories, spontaneous symmetry breakdown and unified theories of weak and electromagnetic interactions. Renormalization group methods, quantum chromodynamics, and nonperturbative approaches to quantum field theory.

[PHYS 631a^u, Computational Physics I.]

PHYS 650a and 651b, Theory of Solids I and II. Simon Mochrie [F], Staff [Sp]. MW 9–10.30 [F], MTh 1–2.30 [Sp]
Theoretical techniques for the study of the structural and electronic properties of solids, with applications. Topics include band structure, phonons, defects, transport, magnetism, and superconductivity. Also ENAS 856a and 857b.

special topics courses

[PHYS 662a, Special Topics in Particle Physics.]

[PHYS 663b, Special Topics in Cosmology and Particle Physics.]

PHYS 664b, Special Topics in Nuclear Physics. Richard Casten.
Emphasis is on nuclear structure. The approach stresses physical ideas, leading to an understanding of a number of advanced nuclear models and to practical case studies with them.

[PHYS 667b, Special Topics in Condensed Matter Physics.]

[PHYS 668b, Special Topics in Geometry and Modern Field Theory.]

PHYS 671a, Special Topics in Nuclear and Particle Physics. John Harris.
Course specializes in relativistic heavy Ion physics with emphasis on understanding the basic physics of the field, techniques utilized, and recent developments.

PHYS 671b, Special Topics in Experimental Nuclear and Particle Physics. Colin Gay.
Propagation of particles and photons in matter, modern detection techniques, types of detectors, large detector systems, accelerators, and seminal experiments are studied. The subject spans the range of energies from low-energy nuclear physics through high-energy physics.

[PHYS 672a or b, Special Topics in Experimental Physics.]

[PHYS 673a or b, Special Topics in Atomic Physics.]

[PHYS 674b, Quantum Information, Quantum Cryptography, and Quantum Computation.]

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