Prerequisites: PHYS GU4021. Formulation of quantum mechanics in terms of state vectors and linear operators, three-dimensional spherically symmetric potentials, the theory of angular momentum and spin, time-independent and time-dependent perturbation theory, scattering theory, and identical particles. Selected phenomena from atomic physics, nuclear physics, and elementary particle physics are described and then interpreted using quantum mechanical models.
Prerequisites: PHYS UN3003 and PHYS UN3007 or the equivalent. Tensor algebra, tensor analysis, introduction to Riemann geometry. Motion of particles, fluid, and fields in curved spacetime. Einstein equation. Schwarzschild solution; test-particle orbits and light bending. Introduction to black holes, gravitational waves, and cosmological models.
Prerequisites: PHYS UN2601 or PHYS UN2802 or the equivalent. This course covers the Standard Model of Particle Physics, including it conception, successes, and limitations, with the goal of introducing upper-level physics majors to the foundations and current status of particle physics as a field of research. Specific topics to be covered include: historical introduction and review of the Standard Model; particle interactions and particle dynamics; relativistic kinematics; Feynman calculus, quantum electrodynamics, quantum chromodynamics, and weak interactions; electroweak unification and the Higgs mechanism; neutrino oscillations; and beyond-standard model physics and evidence. Along the way, students will research special topics and familiarize themselves with particle physics research.
The “Quantum Simulation and Computing Lab” will give students in the Quantum Masters program hands-on experience in quantum optics, quantum simulation and quantum computing. The course combines lectures, tutorials, and two lab sections. In one lab section, students will do experiments with entangled photons. In the second lab section, students will program quantum computers and run algorithms on them using the IBM Qiskit platform.
The course starts with a recap of linear algebra and quantum mechanics, followed by an introduction to quantum optics and quantum information. Two-level systems, Bloch sphere, quantum gates, and elementary quantum algorithms will be discussed. Quantum teleportation and quantum key distribution will be introduced as applications of entanglement. The lecture content will be directly applied in experiments with entangled photons. In the following, state-of-the-art quantum algorithms will be discussed, related to cutting-edge research results in quantum computing. This includes quantum Fourier transform, quantum simulation of the Schroedinger equation, and the variational quantum eigensolver (VQE) algorithm. During the course students will do one experimental project with entangled photons and one quantum programming project. Students will be guided to implement a quantum algorithm of their choice and run it on a quantum computer (IBM, IonQ, QuEra).
Prerequisites: a strong undergraduate background in E-M and classical mechanics. Qualified undergraduates may be admitted with the instructors permission. The basic physics of high energy astrophysical phenomena. Protostars, equations of stellar structure; radiative transfer theory; stellar nucleosynthesis; radiative emission processes; equations of state and cooling theory for neutron stars and white dwarfs, Oppenheimer-Volkoff equation; Chandrasekhar limit; shocks and fluids; accretion theory for both disks and hard surfaces; black hole orbits and light bending.
Prerequisites: PHYS W4021-W4022, or their equivalents. Applications to atoms and molecules, including Thomas-Fermi and Hartree-Fock atoms; interaction of radiation with matter; collision theory; second quantization.
Lagrangian density formalism of Lorentz scalar, Dirac and Weyl spinor, and vector gauge fields. Action variations, symmetries, conservation laws. Canonical quantization, Fock space. Interacting local fields, temporal evolution. Wicks theorem, propagators, and vertex functions, Feynman rules and diagrams. Scattering S matrix examples with tree level amplitudes. Path quantization. 1-loop intro to renormalization.
Course Summary: the quantum many-body problem and its the conceptual formulation in terms of functional integrals, the basics of perturbative calculations at both zero and non-zero temperature, mean field theory and its interpretation as a saddle point of a functional integral, fluctuations including collective modes, the field theory of linear response and transport calculations and the new features associated with nonequilibrium physics.
Recent progress in control of atoms with lasers has led to creating the coldest matter in the universe, constructing ultra precise time and frequency standards, and capability to test high energy theories with tabletop experiments. This course will cover the essentials of atomic physics including the resonance phenomenon, atoms in magnetic and electric fields, and light-matter interactions. These naturally lead to line shapes and laser spectroscopy, as well as to a variety of topics relevant to modern research such as cooling and trapping of atoms. It is recommended for anyone interested in pursuing research in the vibrant field of atomic, molecular, and optical (AMO) physics, and is open to interested students with a one year background in quantum mechanics. Both graduate students and advanced undergraduates are welcome.
Prerequisites: PHYS E6081 or the instructors permission. Semiclassical and quantum mechanical electron dynamics and conduction; dielectric properties of insulators; semiconductors; defects; magnetism; superconductivity; low-dimensional structures; soft matter.
Prerequisites: PHYS G6092. This course will study the classical field theories used in electromagnetism, fluid dynamics, plasma physics, and elastic solid dynamics. General field theoretic concepts will be discussed, including the action, symmetries, conservation laws, and dissipation. In addition, classical field equations will be analyzed from the viewpoint of macroscopic averaging and small-parameter expansions of the fundamental microscopic dynamics. The course will also investigate the production and propagation of linear and nonlinear waves; with topics including linearized small-amplitude waves, ordinary and extraordinary waves, waves in a plasma, surface waves, nonlinear optics, wave-wave mixing, solitons, shock waves, and turbulence.
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