Physics
35 Sloane Physics Laboratory, 432.3607
www.yale.edu/physics/
M.S., M.Phil., Ph.D.
Chair
C. Megan Urry
Director of Graduate Studies
Simon Mochrie (35 SPL, 432.3607, graduatephysics@yale.edu)
Professors
Robert Adair (Emeritus), Charles Ahn (Applied Physics), Yoram Alhassid, Thomas Appelquist, Charles Bailyn (Astronomy), O. Keith Baker, Charles Baltay, Sean Barrett, Cornelius Beausang (Adjunct), William Bennett, Jr. (Emeritus), Richard Casten, Richard Chang (Applied Physics), Paolo Coppi (Astronomy), David DeMille, Michel Devoret (Applied Physics), Frank Firk (Emeritus), Paul Fleury (Applied Physics), Moshe Gai (Adjunct), Steven Girvin, Leonid Glazman, Robert Grober (Applied Physics), Martin Gutzwiller (Adjunct), John Harris, Victor Henrich (Applied Physics), Arvid Herzenberg (Emeritus), Jay Hirshfield (Adjunct), Francesco Iachello, Martin Klein (Emeritus), Henry Kraybill (Emeritus), Steven Lamoreaux, William Lichten (Emeritus), Samuel MacDowell (Emeritus), William Marciano (Adjunct), Simon Mochrie, Vincent Moncrief, Peter Parker, Daniel Prober (Applied Physics), Nicholas Read, Vladimir Rokhlin (Computer Science; Mathematics), Jack Sandweiss, Michael Schmidt, Robert Schoelkopf (Applied Physics), Ramamurti Shankar, Charles Sommerfield (Emeritus), A. Douglas Stone (Applied Physics), Paul Tipton, John Tully (Chemistry), Thomas Ullrich (Adjunct), C. Megan Urry, Pieter van Dokkum (Astronomy), John Wettlaufer (Geology & Geophysics), Robert Wheeler (Emeritus), Werner Wolf (Emeritus), Michael Zeller
Associate Professors
Jerzy Blawzdziewicz (Mechanical Engineering), Karyn LeHur, Priyamvada Natarajan (Astronomy), Corey O’Hern (Mechanical Engineering), Witold Skiba
Assistant Professors
Helen Caines, Eric Dufresne (Mechanical Engineering), Richard Easther, Bonnie Fleming, Steven Furlanetto, Walter Goldberger, Jack Harris, Andreas Heinz, Sohrab Ismail-Beigi (Applied Physics), Daniel McKinsey, Jill North (Philosophy), A. Elizabeth Rhoades (Molecular Biophysics & Biochemistry), Volker Werner
Fields of Study
Fields include atomic physics and quantum optics; nuclear physics; particle physics; astrophysics and cosmology; condensed matter; biological physics; quantum information physics; applied physics; and other areas in collaboration with faculties of Engineering and Applied Science, Mathematics, Chemistry, Molecular Biophysics and Biochemistry, 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 (Classical Mechanics, 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 a required course in quantum field theory, provides an introduction to modern physics and research. Certain equivalent course work may reduce the course requirement or allow substitution of elective courses 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 taking a course offered by the department or by carrying out an approved Special Investigation with individual faculty.
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.
There is no foreign language requirement. Teaching experience is regarded as an integral part of the graduate training program. During their study students are expected to serve as teaching fellows, 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. Students who have successfully advanced to candidacy qualify for the M.Phil. degree.
M.S. (en route to the PH.D.). Students who complete the first-year graduate courses with a satisfactory record (including 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, Classical Mechanics. Francesco Iachello.
MW 11.35–12.50
Newtonian dynamics, Lagrangian dynamics, and Hamiltonian dynamics. Rigid bodies and Euler equations. Oscillations and eigenvalue equations. Classical chaos. Introduction to dynamics of continuous systems.
PHYS 502b, Electromagnetic Theory I. Vincent Moncrief.
MW 9–10.15
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. Andreas Heinz and staff.
HTBA
A laboratory course with experiments and data analysis in soft and hard condensed matter, nuclear and elementary particle physics.
PHYS 506au,Mathematical Methods of Physics. Richard Easther.
MW 9–10.15
Survey of mathematical techniques useful in physics. Includes vector and tensor analysis, group theory, complex analysis (residue calculus, method of steepest descent), differential equations and Green’s functions, and selected advanced topics.
PHYS 508a, Quantum Mechanics I. Jack Harris.
TTh 9–10.15
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. Leonid Glazman.
TTh 11.35–12.50
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.]
PHYS 522a, Introduction to Atomic Physics. David DeMille.
TTh 11.35–12.50
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 523a, Biological Physics. Simon Mochrie.
TTh 2.30–3.45
An introduction to the physics of biological systems, including molecular motors, protein folding, membrane self-assembly, ion pumping, and bacterial locomotion. Background concepts in probability and statistical mechanics are introduced as necessary, as well as key constituents of living cells. Also MB&B 523a.
PHYS 524a, Introduction to Nuclear Physics. Richard Casten.
TTh 11.35–12.50
Introduction to a wide variety of topics in nuclear structure, nuclear reactions, and the emerging new area in nuclear physics of exotic and weakly bound nuclei far from the valley of stability. A number of nuclear models are discussed. The course also covers topics in nuclear astrophysics and in the use of relativistic heavy ion collisions to study quark-gluon interactions at high 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. It is accessible to advanced undergraduates.
PHYS 525a, Quantum Physics at Femto- and Nano-Scales. Dmitri Kharzeev.
W 2.30–4.30
Classical and quantum field theories, symmetries and their breakdown, dynamics of collective excitations, renormalization group, weak coupling methods, quasi-classical approximation, topological effects, phase transitions, and critical phenomena. A wide range of examples and applications are presented, including Quantum Chromo-Dynamics, quark-gluon plasma, nuclear structure, nanoscale systems (especially graphene and carbon nano-tubes), physics of black holes, and the Early Universe.
[PHYS 526b, Introduction to Elementary Particle Physics.]
PHYS 538a, Introduction to Relativistic Astrophysics and General Relativity. Walter Goldberger.
MW 9–10.15
Basic concepts of differential geometry (manifolds, metrics, connections, geodesics, curvature); Einstein’s equations and their application to such areas as cosmology, gravitational waves, black holes.
PHYS 548au and 549bu,Solid State Physics I and II. Charles Ahn.
TTh 1–2.15
A two-term sequence covering the principles underlying the electrical, thermal, magnetic, and optical properties of solids, including crystal structures, phonons, energy bands, semiconductors, Fermi surfaces, magnetic resonance, phase transitions, and superconductivity. Also ENAS 850au,851bu.
[PHYS 570au,High-Energy Astrophysics.]
[PHYS 600b, Cosmology.]
[PHYS 602a, Classical Field Theory.]
PHYS 608b, Quantum Mechanics II. Jack Harris.
TTh 9–10.15
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. Thomas Appelquist.
TTh 11.35–12.50
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 610a, Quantum Many-Body Theory. Yoram Alhassid.
TTh 11.35–12.50
Second quantization, quantum statistical mechanics, Hartree-Fock approximation, linear response theory, random phase approximation, perturbation theory and Feynman diagrams, Landau theory of Fermi liquids, BCS theory, Hartree-Fock-Bogoliubov method. Applications to solids and finite-size systems such as quantum dots, nuclei, and nanoparticles. Also ENAS 852a.
PHYS 624bu,Group Theory. Francesco Iachello.
MW 9–10.15
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 628b, Statistical Physics II.]
PHYS 630b, Relativistic Field Theory II. Thomas Appelquist.
MW 11.35–12.50
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 632b, Quantum Many-Body Theory II. Karyn LeHur.
TTh 9–10.15
A second course in quantum many-body theory, covering the core physics of electron systems, with emphasis on the electron-electron interaction, on the role of dimensionality, on the coupling either to magnetic impurities leading to the well-known Kondo effect or to the electromagnetic noise. Applications to mesoscopic systems and cold atomic gases are also developed.
[PHYS 633b, Introduction to Superconductivity.]
PHYS 634a, Mesoscopic Physics. Michel Devoret.
MW 9–10.15
Introduction to the physics of nanoscale solid state systems that 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.]
[PHYS 651b, Theory of Solids II.]
Special Topics Courses
[PHYS 661b, The Art of Data Analysis.]
PHYS 662b, Special Topics in Particle Physics: Beyond the Standard Model. Walter Goldberger.
MW 11.35–12.50
Modern concepts in particle physics, including electroweak symmetry breaking, mass generation, conformal symmetry, strongly coupled quantum field theories, supersymmetry, and extra dimensions. Material covered includes the theoretical basis of these ideas, experimental tests and constraints, and implications for cosmology.
[PHYS 677a, Noise, Dissipation, Amplification, and Information.]
[PHYS 678b, Computing for Scientific Research.]
PHYS 680au,The Experiments of General Relativity. Jack Sandweiss.
MW 1–2.15
The basic physical ideas and mathematical formulation of general relativity are reviewed, although many results that apply to particular experiments are given without proof. The modern experiments that make precision tests of the theory are explained. These include lunar laser ranging, radar timing from planet Venus reflections, and gravitational radiation from a binary pulsar. A discussion of the LIGO experiment (earth-based gravity wave detector) and LISA (space-based gravity wave detector) is conducted. The course is open to upper-level undergraduates as well as graduate students.
PHYS 990a and b, Special Investigations. Faculty.
Directed research by arrangement with individual faculty members and approved by the DGS.
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