Physics
35 Sloane Physics Laboratory, 203.432.3650
http://physics.yale.edu
M.S., M.Phil., Ph.D.
Chair
Sarah Demers
Director of Graduate Studies
Helen Caines (helen.caines@yale.edu)
Professors Charles Ahn (Applied Physics), Yoram Alhassid, Thomas Appelquist, Charles Bailyn (Astronomy), O. Keith Baker, Charles Baltay (Emeritus), Sean Barrett, Joerg Bewersdorf (Cell Biology), Helen Caines, Hui Cao (Applied Physics), Richard Casten (Emeritus), Flavio Cavanna (Adjunct), Paolo Coppi (Astronomy), Sarah Demers, Thierry Emonet (Molecular, Cellular, and Developmental Biology), Paul Fleury (Emeritus), Marla Geha (Astronomy), Steven Girvin, Larry Gladney, Leonid Glazman, Walter Goldberger, Jack Harris, John Harris (Emeritus), Karsten Heeger, Victor Henrich (Emeritus), Jonathon Howard (Molecular Biophysics and Biochemistry), Francesco Iachello (Emeritus), Sohrab Ismaill-Beigi (Applied Physics), Steve Lamoreaux, Konrad Lehnert, Andre Levchenko (Biomedical Engineering), Reina Maruyama, Simon Mochrie, Vincent Moncrief, Daisuke Nagai, Priyamvada Natarajan (Astronomy), Andrew Neitzke (Mathematics), Corey O’Hern (Mechanical Engineering and Materials Science), Vidvus Ozolins (Applied Physics), Ornella Palamara (Adjunct), Peter Parker (Emeritus), Daniel Prober (Applied Physics), Nicholas Read, Robert Schoelkopf (Applied Physics), John Schotland (Mathematics), Jurgen Schukraft (Adjunct), Ramamurti Shankar, Witold Skiba, A. Douglas Stone (Applied Physics), Hong Tang (Engineering), Paul Tipton, Thomas Ullrich (Adjunct), C. Megan Urry, Frank van den Bosch (Astronomy), Pieter van Dokkum (Astronomy), John Wettlaufer (Earth and Planetary Sciences), Robert Wheeler (Emeritus), Werner Wolf (Emeritus), Michael Zeller (Emeritus)
Associate Professors Damon Clark (Molecular, Cellular, and Developmental Biology), David C. Moore, Michael Murrell (Biomedical Engineering), Nir Navon, Laura Newburgh, Nikhil Padmanabhan, David Poland, Peter Rakich (Applied Physics), Alison Sweeney
Assistant Professors Charles Brown, Meng Cheng, Eduardo da Silva Neto, Laura Havener, Yu He (Applied Physics), Christopher Lynn, Benjamin Machta, Owen Miller (Applied Physics), Chiara Mingarelli, Ian Moult, Shruti Puri (Applied Physics), Diana Qiu (Mechanical Engineering and Materials Science)
Lecturers Mehdi Ghiassi-Nejad, Caitlin Hansen, Stephen Irons, Steven Konezny, Rona Ramos, Adriane Steinacker
Fields of Study
Fields include Astrophysics and Cosmology; Atomic, Molecular and Optical Physics; Biological Physics; Condensed Matter; Gravitational Physics; Nuclear Physics; Particle Physics; Quantum Physics; and other areas in collaboration with the School of Engineering & Applied Science and the departments of Applied Physics; Astronomy; Chemistry; Earth and Planetary Sciences; Molecular Biophysics and Biochemistry; and Molecular, Cellular, and Developmental Biology.
Integrated Graduate Program in Physical and Engineering Biology (PEB)
Students applying to the Ph.D. program in Physics with a concentration in Biological Physics may also apply to the PEB program. See the description under Non-Degree-Granting Programs, Councils, and Research Institutes for course requirements and https://peb.yale.edu for more information about the benefits of this program and application instructions.
Quantum Materials Science and Engineering Certificate (QMSE)
Students applying to the Ph.D. program in Physics with a concentration in quantum materials can apply to the Quantum Materials Science and Engineering (QMSE) certificate program. See the description under Non-Degree-Granting Programs, Councils, and Research Institutes for course requirements and https://qmse.yale.edu for more information about the benefits of the program and application instructions.
Special Requirements for the Ph.D. Degree
To complete the course requirements, students are expected to take one research course, two seminar courses, and a set of seven credit-hour courses: six foundational courses and one elective.
| Six Core Courses | ||
| PHYS 5000 | Advanced Classical Mechanics | 1 |
| PHYS 5020 | Electromagnetic Theory I | 1 |
| PHYS 5060 | Mathematical Methods of Physics | 1 |
| PHYS 5080 | Quantum Mechanics I | 1 |
| PHYS 5100 | Quantum Mechanics II | 1 |
| PHYS 5120 | Statistical Physics I | 1 |
These six courses serve to complete a student’s undergraduate core training in classical and quantum physics. For the seventh course, students may select from the list of graduate elective courses offered by the Departments of Physics or Applied Physics. Courses offered by other departments may also qualify as advanced electives, with the approval of the director of graduate studies (DGS).
Students entering the program with a prior master’s degree may waive core course requirements. Students without a previous master’s can take a core course pass-out exam at the start of the course’s term. Those who successfully demonstrate knowledge of the course topics are excused from taking that core course but must replace the credit hours with an approved advanced elective.
In addition to the core courses, all students must engage in a PHYS 9900, Special Investigations, research project by the end of their second year of study. Incoming students are also required to take PHYS 5150, Topics in Modern Physics Research, in the fall, and PHYS 5900, Responsible Conduct in Research for Physical Scientists in the spring.
By the end of a student’s third year, they must participate in a two-part qualifying event. Part one is a Research Qualifying Event (RQE) consisting of an oral presentation on research completed during their required PHYS 9900, Special Investigation course. Students will present their research and be evaluated on their presentation by the DGS and their research adviser. Part two is a Written Qualifying Event (WQE) consisting of four written components on classical mechanics, electromagnetic theory, statistical mechanics, and quantum mechanics. Each portion of the WQE should be completed after the student has taken, or passed out of, the relevant courses. Students will receive feedback after each portion of the qualifying event. The RQE and WQE are not graded but rather serve as learning milestones. Students may take the qualifying events in any order.
Before starting their fourth year of study, students must submit their thesis prospectus, as presented to and approved by their core thesis committee. Students who have completed their required course credits with satisfactory grades (two Honors and an overall High Pass average), taken the qualifying events, and submitted an acceptable thesis prospectus are recommended for advancement to candidacy and to receive their M.S. and M.Phil en route. Students entering the program with a master’s degree in physics or a related field may waive equivalent graduate-level core courses with approval from the DGS without the requirement of replacing course credits. Students who have waived courses will advance to candidacy but will not receive an M.S. en route from the department.
The teaching experience is regarded as an integral part of the graduate training program. Students are expected to serve four terms as teaching fellows during their studies, usually in the first two years. Students needing additional funding support from the graduate school may be required to teach additional terms. Students who have completed their teaching requirements may also volunteer to teach for additional pay with prior approval from their primary adviser and the DGS.
There is no foreign language requirement in the physics program. However, non-native English speakers who received a score of 25 or below on the TOEFL Speaking section or a 7.5 or below on the IELTS Speaking section are required to participate in a Summer English Language program at Yale in August before matriculation. These students are required to demonstrate English proficiency before they are permitted to teach.
Formal association with a dissertation adviser typically begins after the second year, once the qualifying events have been passed and the required coursework completed. An adviser from a department other than Physics can be chosen in consultation with the DGS, provided the dissertation topic is deemed suitable for a physics Ph.D.
Master’s Degrees
M.Phil. Students who have successfully presented their prospectus and advanced to candidacy qualify for the M.Phil. degree.
M.S. Terminal M.S. degrees are only awarded to students withdrawing from the Ph.D. program after meeting the course requirements but before submitting a thesis prospectus. Requirements for the terminal M.S. are the successful completion of all six core courses listed above, in addition to completing either Special Investigations or an advanced elective (all with a satisfactory record). Students receiving their M.S. en route must have completed all coursework, including PHYS 9900 and an advanced elective. Unless otherwise requested, M.S. en route degrees are awarded once the student has advanced to candidacy.
Additional program information can be found on the Physics website under Academics—Graduate Studies.
Courses
PHYS 5000a, Advanced Classical Mechanics Jack Harris
Newtonian dynamics, Lagrangian dynamics, and Hamiltonian dynamics. Rigid bodies and Euler equations. Oscillations and eigenvalue equations. Classical chaos. Introduction to dynamics of continuous systems.
TTh 11:35am-12:50pm
PHYS 5020b, Electromagnetic Theory I David Moore
Classical electromagnetic theory including boundary-value problems and applications of Maxwell equations. Macroscopic description of electric and magnetic materials. Wave propagation.
MW 11:35am-12:50pm
PHYS 5060a, Mathematical Methods of Physics Chiara Mingarelli
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.
MW 10am-11:15am
PHYS 5080a, Quantum Mechanics I Benjamin Machta
The principles of quantum mechanics with application to simple systems. Canonical formalism, solutions of Schrödinger’s equation, angular momentum, and spin.
MW 1:05pm-2:20pm
PHYS 5100b, Quantum Mechanics II Leonid Glazman
Approximation methods, scattering theory, and the role of symmetries. Relativistic wave equations. Second quantized treatment of identical particles. Elementary introduction to quantized fields.
MW 10am-11:15am
PHYS 5120b, Statistical Physics I Yoram Alhassid
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, enormalization group, irreversible processes, fluctuations.
TTh 11:35am-12:50pm
PHYS 5150a, Topics in Modern Physics Research Sarah Demers and Karsten Heeger
A comprehensive introduction to the various fields of physics research carried out in the department and a formal introduction to scientific reading, writing, and presenting.
F 11:35am-12:50pm
PHYS 5220b, Introduction to Atomic Physics Nir Navon
The course is intended to develop basic theoretical tools needed to understand current research trends in the field of atomic physics. Emphasis is given to laser-spectroscopic methods including laser cooling and trapping. Experimental techniques discussed when appropriate.
TTh 1:05pm-2:20pm
PHYS 5230b / CB&B 5230b / ENAS 5410b / MB&B 5230b / MSCI 5410b, Biological Physics Yimin Luo
This course has three aims: (1) to introduce students to the physics of biological systems, (2) to introduce students to the basics of scientific computing, and (3) to familiarize students with characterization methods and analysis tools. We focus on studies of a broad range of biophysical phenomena including diffusion, polymer statistics, entropic forces, membranes, and cell motion using computational tools and methods. We provide intensive tutorials for Matlab including basic syntax, arrays, functions, plotting, and importing and exporting data.
TTh 2:35pm-3:50pm
PHYS 5380a, Introduction to Relativistic Astrophysics and General Relativity Daisuke Nagai
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.
MW 1:05pm-2:20pm
PHYS 5480a / APHY 5480a / MSCI 5480a, Solid State Physics I Yu He
A two-term sequence (with APHY 5490) 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.
MW 11:35am-12:50pm
PHYS 5490b / APHY 5490b / MSCI 5490b, Solid State Physics II Vidvuds Ozolins
A two-term sequence (with APHY 548) 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.
MW 11:35am-12:50pm
PHYS 5610a / MB&B 5310a / MCDB 5310a, Modeling Biological Systems I Thierry Emonet and Kathryn Miller-Jensen
Biological systems make sophisticated decisions at many levels. This course explores the molecular and computational underpinnings of how these decisions are made, with a focus on modeling static and dynamic processes in example biological systems. This course is aimed at biology students and teaches the analytic and computational methods needed to model genetic networks and protein signaling pathways. Students present and discuss original papers in class. They learn to model using MatLab in a series of in-class hackathons that illustrate the biological examples discussed in the lectures. Biological systems and processes that are modeled include: (1) gene expression, including the kinetics of RNA and protein synthesis and degradation; (2) activators and repressors; (3) the lysogeny/lysis switch of lambda phage; (4) network motifs and how they shape response dynamics; (5) cell signaling, MAP kinase networks and cell fate decisions; and (6) noise in gene expression. Prerequisites: MATH 115 or 116, BIOL 101–104, or with permission of instructors. This course also benefits students who have taken more advanced biology courses (e.g. MCDB 200, MCDB 310, MB&B 300/301).
TTh 2:35pm-3:50pm
PHYS 5620b / CB&B 5620b / ENAS 5620b / INP 7562b / MB&B 5620b / MCDB 5620b, Modeling Biological Systems II Thierry Emonet and Harry McNamara
This course covers advanced topics in computational biology. How do cells compute, how do they count and tell time, how do they oscillate and generate spatial patterns? Topics include time-dependent dynamics in regulatory, signal-transduction, and neuronal networks; fluctuations, growth, and form; mechanics of cell shape and motion; spatially heterogeneous processes; diffusion. This year, the course spends roughly half its time on mechanical systems at the cellular and tissue level, and half on models of neurons and neural systems in computational neuroscience. Prerequisite: a 2000-level biology course or permission of the instructor.
TTh 2:35pm-3:50pm
PHYS 5700b / ASTR 5700b / PHYS 570, High-Energy Astrophysics Paolo Coppi
A survey of current topics in high-energy astrophysics, including accreting black hole and neutron star systems in our galaxy, pulsars, active galactic nuclei and relativistic jets, gamma-ray bursts, and ultra-high-energy cosmic rays. The basic physical processes underlying the observed high-energy phenomena are also covered.
MW 2:35pm-3:50pm
PHYS 5710a / ENAS 5710a / MB&B 5910a / MCDB 5910a, Integrated Workshop Corey O'Hern
This required course for students in the PEB graduate program involves a series of modules, co-taught by faculty, in which students from different academic backgrounds and research skills collaborate on projects at the interface of physics, engineering, and biology. The modules cover a broad range of PEB research areas and skills. The course starts with an introduction to MATLAB, which is used throughout the course for analysis, simulations, and modeling.
TTh 9am-10:15am
PHYS 5900b / APHY 5900b, Responsible Conduct in Research for Physical Scientists Sarah Demers
A review and discussion of best practices of conduct in research including scientific integrity and misconduct; mentorship; data management; and diversity, equity, and inclusion in science.
F 10am-11:15am
PHYS 6010a / APHY 6600a, Quantum Information and Computation Aleksander Kubica
This course focuses on the theory of quantum information and computation. We cover the following tentative list of topics: overview of postulates of quantum mechanics and measurements, quantum circuits, physical implementation of quantum operations, introduction to computational complexity, quantum algorithms (DJ, Shor’s, Grover’s, and others as time permits), decoherence and noisy quantum channels, quantum error-correction and fault-tolerance, stabilizer formalism, error-correcting codes (Shor, Steane, surface-code, and others as time permits), quantum key distribution, quantum Shannon theory, entropy, and data compression.
TTh 11:35am-12:50pm
PHYS 6100a / APHY 6100a, Quantum Many-Body Theory Yoram Alhassid
Identical particles and second quantization. Electron tunneling and spectral function. General linear response theory. Approximate methods of quantum many-body theory. Dielectric response, screening of long-range interactions, electric conductance, collective modes, and photon absorption spectra. Fermi liquid; Cooper and Stoner instabilities; notions of superconductivity and magnetism. BCS theory, Josephson effect, and Majorana fermions in condensed matter; superconducting qubits. Bose-Einstein condensation; Bogoliubov quasiparticles and solitons.
TTh 2:35pm-3:50pm
PHYS 6120a / APHY 6280a, Statistical Physics II Nicholas Read
An advanced course in statistical mechanics. Topics may include mean field theory of and fluctuations at continuous phase transitions; critical phenomena, scaling, and introduction to the renormalization group ideas; topological phase transitions; dynamic correlation functions and linear response theory; quantum phase transitions; superfluid and superconducting phase transitions; cooperative phenomena in low-dimensional systems.
TTh 2:35pm-3:50pm
PHYS 6200a, Relativistic Field Theory I Ian Moult
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.
MW 11:35am-12:50pm
PHYS 6300b, Relativistic Field Theory II David Poland
An introduction to non-Abelian 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.
TTh 9am-10:15am
PHYS 6500a / APHY 6500a, Theory of Solids I Leonid Glazman
A graduate-level introduction with focus on advanced and specialized topics. Knowledge of advanced quantum mechanics (Sakurai level) and solid state physics (Kittel and Ashcroft-Mermin level) is assumed. The course teaches advanced solid state physics techniques and concepts.
T 3:30pm-5:30pm
PHYS 6650a, Graduate Research Seminar Ramamurti Shankar
Seminar research presentations by graduate students. Prerequisite: knowledge of introductory graduate course material.
Th 2:30pm-4pm
PHYS 6700b, Special Topics in Biophysics Christopher Lynn
The aim of the course is to introduce students to the approaches, methods, major results, and open questions in modern biological physics. Topics include non-equilibrium statistical physics, with applications to kinetic proof-reading and understanding molecular motors, information theory with applications to cellular signaling and phase transitions as they occur in living systems. The course is designed for graduate students in physics or a closely related field, otherwise, permission of the instructor is required.
Th 3:30pm-5:30pm
PHYS 6750a / APHY 6750a, Principles of Optics with Applications Hui Cao
Introduction to the principles of optics and electromagnetic wave phenomena with applications to microscopy, optical fibers, laser spectroscopy, nanophotonics, plasmonics, and metamaterials. Topics include propagation of light, reflection and refraction, guiding light, polarization, interference, diffraction, scattering, Fourier optics, and optical coherence.
HTBA
PHYS 6760a / APHY 6760a, Introduction to Light-Matter Interactions Peter Rakich
Optical properties of materials and a variety of coherent light-matter interactions are explored through the classical and quantum treatments. The role of electronic, phononic, and plasmonic interactions in shaping the optical properties of materials is examined using generalized quantum and classical coupled-mode theories. The dynamic response of media to strain, magnetic, and electric fields is also treated. Modern topics are explored, including optical forces, photonic crystals, and metamaterials; multi-photon absorption; and parametric processes resulting from electronic, optomechanical, and Raman interactions.
MW 4pm-5:15pm
PHYS 6910a / APHY 6910a, Quantum Optics Shruti Puri
Quantization of the electromagnetic field, coherence properties and representation of the electromagnetic field, quantum phenomena in simple nonlinear optics, atom-field interaction, stochastic methods, master equation, Fokker-Planck equation, Heisenberg-Langevin equation, input-output formulation, cavity quantum electrodynamics, quantum theory of laser, trapped ions, light forces, quantum optomechanics, Bose-Einstein condensation, quantum measurement and control.
TTh 2:35pm-3:50pm
PHYS 9900a or b, Special Investigations Staff
Directed research by arrangement with individual faculty members and approved by the DGS in a student's second year. Students are expected to propose and complete a term-long research project. The culmination of the project is a presentation that fulfills the departmental requirement for the research qualifying event.
HTBA