# Physics Graduate Course List

Quantum computing and other quantum information technologies. Differences between bit and qubit. Quantum logic gates, concept of entanglement, quantum teleportation, quantum cryptography and key distribution, quantum computing algorithms, including Deutsch-Jozsa algorithm, Grover’s search algorithm, Shor’s factoring algorithm. Basics of public-key cryptosystems and number theory as needed to present Shor’s algorithm. Errors in a quantum computer and quantum error correction.

Quantum optics and quantum bit (qubit) platforms for quantum technology applications. Qubit as physical system, quantum unitary evolution as quantum gate, quantum control using electromagnetic fields, Rabi oscillations, adiabatic theorem, density matrix, Liouville-von Neumann equation, decay and decoherence (T1 and T2), spin echo, Ramsey interferometry, coherent population trapping, entanglement, dynamical maps, electromagnetic field quantization, Jaynes-Cummings Hamiltonian, spontaneous emission, solid-state qubit platforms (spin qubits, superconducting qubits), atomic qubit platforms (trapped ions), color-centers in solids.

Theory of classical Lagrangian and Hamiltonian mechanics of particles and rigid bodies, including canonical transformations and Hamilton-Jacobi theory.

Classical theory of electromagnetism and its applications. Electrostatics and magnetostatics; Maxwells equations and electromagnetic waves; wave guides, apertures, and antennae.

Classical theory of electromagnetism and its applications. Special relativity and Lagrangian and Hamiltonian formulations; Lienard-Wiechert potentials, motion, radiation, and energy loss be charged particles; self-fields and radiative damping; magnetic monopoles and field theories.

General principles of nonrelativistic quantum mechanics from the point of view of advanced dynamics, with applications to problems of atomic and nuclear structure

General principles of nonrelativistic quantum mechanics from the point of view of advanced dynamics, with applications to problems of atomic and nuclear structure.

Solidity, crystal structure, k-space, quantum mechanics of covalent bonding, phonon excitations, thermal energy, the nearly-free-electron approximation, Bloch electrons, E(k) energy bands in semiconductors and metals, density of states, optical properties of solids, donors and acceptors in semiconductors, excitons, plasmons, polaritons, electrical properties, magnetic materials, the percolation model and phase transitions, metal-insulator transitions, and amorphous solids.

Solidity, crystal structure, k-space, quantum mechanics of covalent bonding, phonon excitations, thermal energy, the nearly-free-electron approximation, Bloch electrons, E(k) energy bands in semiconductors and metals, density of states, optical properties of solids, donors and acceptors in semiconductors, excitons, plasmons, polaritons, electrical properties, magnetic materials, the percolation model and phase transitions, metal-insulator transitions, and amorphous solids.

Introduction to the field of polymer physics. Statistical descriptions of polymers based on Brownian motion and random walk models. Conformation of single chains. Thermodynamics of polymer mixtures, solutions, and melts. Properties of polymer networks. Polymer dynamics in both melt and solution states

Methods of controlling matter on the nanometer length scale and the applications thereof. Nanolithography, self-assembly, and scanned probe microscopy; nanomaterials including fullerenes, carbon nanotubes, and quantum dots; nanoscale and molecular electronics; nanoelectromechanical systems; nanoscale optoelectronics; and nanobiotechnology

Theory of laser oscillation, optical resonators, interaction of radiation and atomic systems, giant pulsed lasers, laser systems, wave propagation in nonlinear media, modulation of optical radiation, noise in optical detection and generation, and interaction of light and sound.

Fundamentals of the ray, wave and quantum models of light, and topics in modern optics with contemporary applications.

Geometric formulation of classical physics. Applications in relativity, optics, elasticity, fluid mechanics, plasma physics. Real-world examples from fundamental, experimental, and applied physics. Quantum roots of and quantum techniques in classical physics. Geometrical connections between classical mechanics, optics, and quantum physics. Problems in and connections between elasticity, fluid dynamics, magnetohydrodynamics, and plasma physics.

Survey of our current understanding of the origin, evolution, and fate of the Universe. Observational evidence behind the idea of the hot Big Bang, including the linear velocity-distance law, the existence of the cosmic microwave background, and the arguments for dark matter. Physics of a dynamic, expanding Universe via the Friedmann-Lemaitre-Robertson-Walker metric. Physical principles to determine the conditions in the early Universe, introducing the idea of inflation. Mechanisms driving the origin and evolution of galaxies and large-scale structures.

Methods and applications of Einsteins general theory of relativity. Space and time and gravity in Newtonian physics; special theory of relativity; gravity as geometry of curved spacetime; black holes; cosmology; Einsteins gravitational field equations; gravitational waves and relativistic stars.

Theory of classical and quantum statistical mechanics. Derivation of thermodynamics. Ensembles, fluctuations and ideal gas systems.

Theory of classical and quantum statistical mechanics. Derivation of thermodynamics. Modern developments and advanced topics.

Selected topics in mathematical physics. Review of analytic function theory. Matrices, spectral theory of operators in Hilbert Space with applications to quantum mechanics. Solution of partial differential equations of mathematical physics, boundary-value problems, and special functions. Distribution theory and Greens functions.

Selected topics from the general area of biomechanics, bioelectricity, radiation biophysics, molecular biophysics, and thermodynamics and transport in biological systems. Emphasis on the physical aspects of biological phenomena and biophysical measurement techniques and instrumentation.

Survey of computational methods in physics. Applications of Fourier analysis, curve fitting, solving differential equations, solving integral equations, Monte Carlo simulations, symbolic mathematics, and graphic simulations in mechanics, electromagnetism, nuclear physics, atomic physics, molecular physics, and condensed matter physics.

Two-part course. Fall semester: Introduction to research opportunities for first-year graduate students in Physics; refinement of research and oral presentation skills. Spring semester: Conducting ethically-sound research in a diverse professional environment; writing for the scientific community. Both parts fulfill Graduate School requirements of ethics and integrity, and diversity and inclusion.

Classical field theory; Noethers theorem and symmetries; second quantization and many-body formalism; free quantum Klein-Gordon, Dirac, and Maxwell fields; and interacting fields, S-matrix and covariant perturbation theory. Feynman diagrams; quantum electrodynamics; renormalization; path-integral formulation; non-Abelian gauge theories; and elements of electro-weak theory.

Classical field theory; Noethers theorem and symmetries; second quantization and many-body formalism; free quantum Klein-Gordon, Dirac, and Maxwell fields; and interacting fields, S-matrix and covariant perturbation theory. Feynman diagrams; quantum electrodynamics; renormalization; path-integral formulation; non-Abelian gauge theories; and elements of electro-weak theory.

Applications of field-theory techniques to many-body aspects of solid-state physics. Green functions, Feynman diagrams, lattice Hamiltonian, neutron scattering, electron gas, Fermi-liquid theory, and linear-response theory. 6556: Electron-phonon interaction in metals and semiconductors, polarons, optical properties, excitons, superconductivity, and excitations in magnetic materials.

Applications of field-theory techniques to many-body aspects of solid-state physics. Electron-phonon interaction in metals and semiconductors, polarons, optical properties, excitons, superconductivity, and excitations in magnetic materials.

Differential geometry; equivalence principle; general theory of relativity; classical tests; post-Newtonian approximation; special solutions.

Black holes; observational basis of cosmology; relativistic model universes; nucleosynthesis; cosmic background radiation; dark matter; inflation.

Topics of current interest in theoretical physics as announced in Timetable. May be repeated for credit with permission.

Symmetry principles, quark model, scattering-theory and particle-theory processes, weak interactions, quantum chromodynamics, spontaneous symmetry breaking, and unified field theories.

Symmetry principles, quark model, scattering-theory and particle-theory processes, weak interactions, quantum chromodynamics, spontaneous symmetry breaking, and unified field theories.