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, Sean Barrett, D. Allan Bromley, Richard Casten, Richard Chang (Applied Physics), Paolo Coppi (Astronomy), David DeMille, 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), Francesco Iachello, Martin Klein, William Marciano (Adjunct), Simon Mochrie, Vincent Moncrief, Peter Parker, Daniel Prober (Applied Physics), Nicholas Read, Subir Sachdev, Jack Sandweiss, Michael Schmidt, Robert Schoelkopf (Applied Physics), Ramamurti Shankar, Charles Sommerfield, A. Douglas Stone (Applied Physics), John Tully (Chemistry), C. Megan Urry, John Wettlaufer (Geophysics), Michael Zeller
Associate Professors
Charles Ahn (Applied Physics), Colin Gay
Assistant Professors
Helen Caines, Richard Easther, Bonnie Fleming, Jack Harris, Andreas Heinz, Sohrab Ismail-Beigi (Applied Physics), Daniel McKinsey, Priyamvada Natarajan (Astronomy), Homer Neal, Corey O'Hern (Mechanical Engineering), Witold Skiba
Senior Research Scientists
Robert Adair, Satish Dhawan, Richard Majka, Andrew Szymkowiak, N. Victor Zamfir
Lecturers
Stephen Irons, Henry Kasha
Fields of Study
Fields include atomic physics; nuclear physics; particle physics; astrophysics and cosmology; condensed matter; quantum information physics; applied physics; and other areas in collaboration with faculties of Engineering and Applied Science, Mathematics, Chemistry, Geology and Geophysics, and Astronomy.
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 (a High Pass average and the Graduate School requirement of two Honors), 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. Students are expected to serve as teaching fellows at some point during their study, usually in the first two years. 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. Francesco Iachello.
MW 1–2.30
Newtonian dynamics, Lagrangian dynamics, and Hamiltonian dynamics. Small oscillations and rigid bodies. Strings, membranes. Fluids.
PHYS 502b, Electromagnetic Theory I. Nicholas Read.
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. Staff.
HTBA
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 506au, Mathematical Methods of Physics. Richard Easther.
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 selected advanced topics.
PHYS 508a, Quantum Mechanics I. Thomas Appelquist.
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 512a, Statistical Physics I. Yoram Alhassid.
TTh 10.30–12
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. Yoram Alhassid.
HTBA
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.
MW 10.30–12
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. The aim is to give a broad perspective on the subject and to develop the key ideas in as simple a way as possible. Physics ideas always have precedence over mathematical formalism. The course assumes no prior knowledge of nuclear physics and only elementary quantum mechanics.
[PHYS 526b, Introduction to Elementary Particle Physics.]
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 548au and 549bu, Solid State Physics I and II. Victor Henrich [F], Robert Schoelkopf [Sp].
TTh 1–2.15 [F], TTh 9–10.15 [Sp]
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 850au, 851bu.
[PHYS 570bu, High-Energy Astrophysics.]
[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. Witold Skiba.
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 624bu, Group Theory. Francesco Iachello.
MW 1–2.20
Lie algebras, Lie groups, and some of their applications. Representation theory. Explicit construction of finite-dimensional irreducible representations. Invariant operators and their eigenvalues. Tensor operators and enveloping algebras. Boson and fermion realizations. Differential realizations. Quantum dynamical applications.
[PHYS 628a, Statistical Physics II.]
PHYS 630b, Relativistic Field Theory II. Witold Skiba.
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 631au, Computational Physics I.]
PHYS 633b, Introduction to Superconductivity. Daniel Prober.
MW 10.30–12
The fundamentals of superconductivity, including both theoretical understandings of basic mechanisms, and description of major applications. Topics include historical overview, Ginzburg-Landau (mean field) theory, critical currents and fields of type II superconductors, BCS theory, Josephson junctions and microelectronic and quantum-bit devices, and high Tc oxide superconductors. Also ENAS 863b.
[PHYS 634a, Mesoscopic Physics.]
PHYS 650a, Theory of Solids I. Sohrab Ismail-Beigi.
WF 10.30–12
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.
[PHYS 651b, Theory of Solids II.]
Special Topics Courses
[PHYS 661b, The Art of Data Analysis.]
[PHYS 662a, Special Topics in Particle Physics.]
PHYS 663b, Special Topics in Cosmology and Particle Physics. Richard Easther.
MW 9–10.30
Introduction to theoretical cosmology, and the physics of the very early universe. The course begins with the “standard model” of the big bang, and current observational constraints on cosmological models. Subsequent topics include inflationary models, the generation of perturbations in the primordial universe, the cosmological implications of string theory, and brane-world models of the universe.
PHYS 664b, Special Topics in Nuclear Physics. Richard Casten.
TTh 9–10.30
The emphasis in this course is on nuclear structure models and their use in understanding atomic nuclei. A number of models are covered, ranging from the Shell Model to a variety of Collective models. In each case, practical calculations are carried out by the students so that the application of these models to real situations, and their strengths, weaknesses, and ranges of applicability, become clear. Finally, there is discussion of the evolution of nuclear structure as a function of nucleon number, both near and far from the valley of stability, the appearance of behavior resembling phase transitions, and simple guidelines to structural evolution.
PHYS 667a, Special Topics in Condensed Matter Physics: Quantum Hall Effect and Conformal Field Theory. Nicholas Read.
MW 10.30–12
Aspects of the quantum Hall effect, particularly the fractional effect, and conformal field theory, plus the connections between the two. Quantum Hall states, composite particles, quasiparticles, fractional charge and statistics. Future applications to rotating trapped atoms. Conformal symmetry in two dimensions, applications to classical critical phenomena, 1+1 quantum field theory. Nonabelian quantum Hall states and the relation with conformal field theory and Chern-Simons gauge theory. Background required: statistical mechanics, and either many-body theory or quantum field theory. Also ENAS 860a.
[PHYS 668b, Special Topics in Geometry and Modern Field Theory.]
PHYS 671b, Special Topics in Experimental Nuclear and Particle Physics. Colin Gay.
MW 10.30–12
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.]
PHYS 675b, Special Topics in Optics. Richard Chang.
TTh 2.30–3.45
A survey of the principles of optics. Topics include geometrical optics, optical imaging, interference, and diffraction. The course is taught from the experimentalist perspective and emphasizes real applications. Also ENAS 859b.
PHYS 676a, Optical Properties of Semiconductors. Richard Chang.
TTh 11.30–12.45
Comprehensive treatment of the optical and electronic properties of semiconductor alloys and quantum structures. Physical models of blackbody radiation, spontaneous emission, stimulated emission, absorption, and polarization. Quantitative analysis of the effects of temperature, pressure, stress fields, and electric and magnetic fields. Also ENAS 917au.
PHYS 677a, Noise, Dissipation, and Amplification. Michel Devoret.
TTh 9–10.30
Graduate-level equilibrium and non-equilibrium statistical physics applied to quantum electronics/optics phenomena. The aim is to explain the fundamental link between the random fluctuations of a physical system in equilibrium and the response of the same system to an external perturbation. Several key examples where noise appears as a resource rather than a limitation are treated: spin relaxation in nuclear magnetic resonance (motional narrowing), Johnson-Nyquist noise in solid state transport physics (noise thermometry), photon correlation measurements in quantum optics (Hanbury Brown-Twiss experiment), and so on. The course explores both passive and active systems. It discusses in particular the ultimate limits of amplifier sensitivity and speed in physics measurements. Also ENAS 817a.
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