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),
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, 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
Cornelius Beausang, David DeMille, Colin Gay, Tilo Wettig
Assistant Professors
Charles Ahn (Applied Physics), Richard Easther, Andreas Heinz,
Homer Neal, Corey O’Hern (Mechanical Engineering), Witold
Skiba, Jeffrey Snyder
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; condensed-matter; quantum information
physics; applied physics; and other areas in collaboration
with faculties of Engineering and Applied Science, Mathematics,
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.
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. 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. 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. 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 506au, 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. 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 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. Yoram
Alhassid. 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. David
DeMille. MW 10.30–12
This course is intended to develop basic theoretical
tools needed to understand fundamental atomic processes. Emphasis
given to applications in laser spectroscopy. Experimental
techniques discussed when appropriate.
PHYS 524a, Introduction to Nuclear Physics. Richard
Casten. MW 1–2.30
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. 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 548au and 549bu, Solid State Physics I and II. Victor
Henrich [F], Robert Schoelkopf [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 850au, 851bu.
[PHYS 570bu, High-Energy Astrophysics.]
PHYS 600b, Cosmology. Priyamvada Natarajan.
The large-scale contents and structure of the universe
and the origin of galaxies. Also ASTR 600b.
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. Subir
Sachdev. F 12.30–3.30
An introduction to topics in the theory of classical
and quantum phase transitions. Order parameters and effective
field theory. Critical phenomena and the renormalization group.
Duality, topological defects and bosonization.
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 634a, Mesoscopic Physics. Michel Devoret.
TTh 9–10.30
Introduction to the physics of nanoscale solid-state
systems which are large and disordered enough to be described
in terms of simple macroscopic parameters like resistance,
capacitance, and inductance, but small and cold enough that
effects usually associated with microscopic particles, like
quantum-mechanical coherence and/or charge quantization, dominate.
Emphasis is placed on transport and noise phenomena in the
normal and superconducting regimes. Also ENAS 818a.
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. Thomas
Ullrich. F 1–3
The course is an introduction to mathematical and statistical
techniques used to analyze data. The course is fairly practice-oriented
and is aimed at students who have, or anticipate having, research
data to analyze in a thorough and unbiased way. It covers
subjects in statistics, computing/numerical techniques, data
analysis, but also topics related to data reconstruction and
pattern recognition which are closely linked to the understanding
of the data derived from those methods. The intention is to
prepare students for a better approach to their own analysis.
Many of the topics covered are related to typical problems
in experimental high-energy and nuclear physics but are fairly
general in nature.
[PHYS 662a, Special Topics in Particle Physics.]
[PHYS 663b, Special Topics in Cosmology and Particle
Physics.]
[PHYS 664b, Special Topics in Nuclear Physics.]
PHYS 667b, Special Topics in Condensed Matter Physics:
Nonequilibrium Dynamics and Pattern Formation. Pierre
Hohenberg. HTBA
Stationary and time-dependent spatial patterns are studied
in extended systems driven away from equilibrium. A variety
of mathematical models are introduced to describe phenomena
such as bifurcations, ordered spatial patterns, defect patterns,
excitability, and spatiotemporal chaos. The predictions of
the models are compared to experiments in fluids (Rayleigh-Benard
convection), oscillatory chemical reactions, electrical excitation
of heart tissue, and other systems. Prerequisites: graduate
courses in statistical physics and mathematical methods. Also
ENAS 860b.
[PHYS 668b, Special Topics in Geometry and Modern Field
Theory.]
[PHYS 671a and b, Special Topics in Nuclear and Particle
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 675a, 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 859a.
[PHYS 676b, Optical Properties of Semiconductors.]
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