A course on topics in nonlinear physics. Finite dimensional flows, bifurcations, instabilities, and relation to phase transitions. Index theory and its use for the classification of topological defects. Chaos, strange attractors, maps, and fractals. To illustrate the nonlinear phenomena studied, we will draw examples from a diverse range of disciplines, including classical and quantum physics, but also chemistry, biology, and social sciences, to list only a few. Numerical exercises will be used throughout the course.

Basis of Einstein's Theory of General Relativity. Topics are as follows. Special relativity and tensors: Galilean relativity and 3-vectors. Special relativity and 4-vectors. Relativistic particles. Electromagnetism. Constant relativistic acceleration. Spacetime: Equivalence principle. Spacetime as a curved manifold. Tensors in curved spacetime. Rules for tensor index gymnastics. The covariant derivative: How basis vectors change: the affine connection. Covariant derivative and parallel transport. Geodesic equations. Spacetime curvature: Curvature and Riemann tensor. Riemann normal coordinates and the Bianchi identity. Information in Riemann. The physics of curvature: Geodesic deviation. Tidal forces. Taking the Newtonian limit. The power of symmetry, and Einstein's equations: Lie derivatives. Killing tensors. Maximally symmetric spacetimes. Einstein's equations. Black hole basics: Birkhoff's theorem and the Schwarzschild solution. TOV equation for a star. Geodesics of Schwarzschild. More advanced aspects of black holes: Causal structure of Schwarzschild. Reissner-Nordstrom black holes. Kerr black holes. The Penrose process. Classic experimental tests of GR: Gravitational redshift. Planetary perihelion precession. Bending of light. Radar echoes. Geodesic precession of gyros. Accretion disks. Gravitational lensing: Behaviour of light in gravitational fields. Deflection angles. Time delay. Magnification and multiple images.

This course follows the Introduction to General Relativity with derivation of Einstein's equation from fundamental action principles, and the study of the application of General Relativity to Astrophysics and Cosmology. We begin by outlining how Einstein's equations can be derived from an action principle from scratch, then discuss possible alternative theories of gravity and extra dimensions. We then discuss the production and detection of gravitational waves as a probe of astrophysical and cosmological phenomena. Next, we develop the story of homogeneous isotropic FRW cosmology, and introduce the idea of inflation. Then we discuss aspects of the thermal physics of the early universe. After that, we give an outline of the theory of inflationary perturbations, how they grow over time, and how this can be read off the cosmic microwave background and directly dictates the formation of large scale structure in our universe today.

This course covers a broad range of advanced topics in classical optics, with the laser as a unifying theme. Topics include atom-photon interactions (absorption, radiation, and stimulated emission), how a laser works (gain, pumping, rate equation models, threshold, and gain clamping), optical resonators (their spectrum, finesse, stability, and transverse modes), propagation of Gaussian beams and paraxial rays, and the statistics of optical fields (spatial and temporal coherence). Time permitting, pulse propagation and pulsed lasers will be discussed.

Introduction to the physics of solids and their electronic and thermal properties. Topics include crystal structure and symmetry, X-ray and neutron diffraction, electronic band structure, lattice vibrations and phonons. Selected advanced topics such as electron interactions and anharmonic effects will be also covered. A good understanding of undergraduate quantum mechanics and statistical mechanics is expected.

This course introduces the basics of fundamental particles and the strong, weak and electromagnetic forces that govern their interactions in the Standard Model of particle physics. Topics include: introduction to the Standard Model, Feynman diagrams, relativistic kinematics, conservation laws, particle decays and scattering processes, fermions and the Dirac equation, electroweak unification and the Higgs field.

Realist, phenomenalist, and pragmatist perspectives on scientific theories. Review of conventional textbook quantum mechanics. Local causality and signal locality. Elements of formal measurement theory and wave function collapse; decoherence and the classical/quantum boundary. Copenhagen interpretation of quantum mechanics. Operationalist quantum mechanics. Hidden variable theories: possibilities and problems. Contextuality and nonlocality; Bell's theorem. Bohm deBroglie theory and generalizations. Modal interpretations and consistent histories quantum mechanics of Gell-Mann, Hartle, Omnes. Relative state interpretations (Everett's "many worlds," more recent work by Wallace and Carroll). Quantum Darwinism. QBism. Relational Quantum Mechanics. A sketch of collapse theories.

This course provides an introduction to the thermodynamics, stability, and dynamics of the terrestrial atmosphere. It represents suitable preparation for research in experimental and theoretical atmospheric physics. It is also relevant for research in oceanography and planetary atmospheres. Topics include hydrostatics, atmospheric vertical structure, dry and moist thermodynamics, stability for small- and large-amplitude displacements, conservation laws, internal gravity waves, geostrophic balance, thermal wind balance, vorticity, circulation, and potential vorticity. Coursework involves analytic and numerical exercises, some observational data analysis, and reviews of papers in the Atmospheric Physics literature.

Brief review of thermodynamics. Topics include: Liouville theorem, Liouville equation, Poincare recurrences. The main postulate of statistical mechanics. Microcanonical and canonical ensembles. Grand canonical distribution and chemical equilibrium. Nonideal classical systems, van der Waals, and the liquid-gas transition. The quantum microcanonical, canonical, and grand canonical distributions. The density matrix: pure and mixed states; the quantum Liouville equation; the use of imaginary time. The quantum ideal gases: general formulae for any statistics. The ideal Fermi gas; examples of applications. The ideal Bose gas: Bose condensation and examples of applications.

An introduction to relativistic electrodynamics. Topics include: special relativity, four-vectors and tensors, relativistic dynamics from the Principle of Stationary Action and Maxwell's equations in Lorentz covariant form. Noether's theorem for fields and the energy-momentum tensor. Fields of moving charges and electromagnetic radiation: retarded potential, Lienard-Wiechert potentials, multipole expansion, radiation reaction.

This core course covers advanced topics in non-relativistic quantum mechanics. Topics may include: Kets, Bras, and Operators; basis sets, Change of Basis and Matrix Representations; Measurements, Observables, and the Uncertainty Relations; Continuous systems: Position, Momentum, and Translation; Density Operators and Pure Versus Mixed Ensembles; entropy; Time Evolution: Schrodinger Equation; Heisenberg Picture; master equation; Schrodinger's Wave Equation; free particles; bound states; examples (square well, HO); Angular Momentum in Quantum Mechanics; Spherical symmetry and the Hydrogen Atom; Symmetries, Conservation Laws, and Degeneracies; Time-Independent Perturbation Theory; fine structure of Hydrogen; scattering; Time-Dependent Perturbation Theory: The Interaction Picture; Fermi's golden rule; Multi-Particle states; Permutation Symmetry and Pauli Principle.

The static, kinematic, and dynamic behaviours of fluids have huge import in physics, astrophysics engineering, earth sciences, and life sciences, and fluid mechanics is a basic scientific literacy in physics education. This course will introduce the fundamental physical principles and ways of thinking of fluid dynamics hand-in-hand with the development of problem solving skills applicable to different domains of fluid mechanics. The course will cover the physics and mathematics of kinematics and dynamics of fluids, including forces, fluxes, and conservation laws. We will illustrate these concepts through a tremendous variety of phenomena that can be understood based on several relatively simple principles encapsulated in mathematical equations of fluid motion. Examples may include steady flows, vorticity, drag and lift, gravity and capillary waves, hydrodynamic instabilities such as Kelvin-Helmholtz instability in the atmosphere and Raleigh-Taylor instability in super-novae, and strange behavior of biological swimmers on the microscale.

An introduction, aimed at the physicist, to various mathematical methods of use in several areas of physics. Topics may include tensor algebra and exterior calculus on manifolds, group theory, and solutions of ordinary and partial differential equations with Green functions.

This course will provide the framework for the development of effective communication skills that will help you, as a scientist, throughout your careers. We will focus on the various ways one communicates to a diversity of audiences. We will start off with a brief introduction to the philosophy of scientific reasoning and its distinction from other means of rationalizing natural phenomena. We will then proceed to looking at what constitutes effective writing, excellent presentations and pursuasive public speaking. Much of our focus will be on what is good scientific writing and what makes a great scientific presentation. These will be developed by practice and by receiving extensive feedback from classmates and the course instructor. The course will also introduce practices that will help you be more effective as a science communicator to a more general audience.

This is a graduate course on research computing, covering techniques and methods for reliable and efficient computational programming. It includes best practices for developing software as it applies to scientific computations, common numerical techniques and packages, and aspects of high performance computing. Topics include version control, modular programming, file handling, debugging, profiling, floating point computations, linear algebra, fast Fourier transforms, solving differential equations, parallel programming and using shared compute clusters. Students are required to have some programming experience in a compiled language (Fortran, C, C++). The course uses C++ as the programming language.

This course will allow for advanced examination of physics topics. Course content in any given year may vary. More than one Special Topics in Physics courses may be taken for credit and will be distinguished in each instance by a subtitle.

This course will allow for advanced examination of physics topics. Course content in any given year may vary. More than one Special Topics in Physics courses may be taken for credit and will be distinguished in each instance by a subtitle.

The goal of this course is to develop an understanding of the structure of atoms and molecules, and shed light on how and why they are used in modern AMO research. The course will assume a strong background in graduate-level electromagnetism and topics from Quantum Optics I. Course content: Structure of atoms and molecules. Angular momentum and parity. Selection rules. Multipole moments. Energy level shifts due to electric and magnetic fields. Spontaneous emission. Branching ratios. Cycling transitions and repumps. Laser cooling. Other topics (scattering, diatomic molecules, relativistic atomic physics) depending on student interest.

This course explores atom-photon interactions with a semi-classical treatment: how does a quantum system respond to a classical drive field? We begin by discussing how an atom driven by an optical field reduces to a dipole interaction Hamiltonian. The atom-photon problem can then be mapped onto a spin one-half electron in a magnetic field, since both are driven two-level quantum systems. We develop the Bloch equations, Rabi oscillations, and magnetic resonance. Returning to the optical regime a treatment using density matrices is necessary to include the effects of damping. Dynamics of the density operator are described by the optical Bloch equations, with which one can understand a wide range of current experiments in atomic, molecular, and optical physics and solid-state physics. These quantum dynamics are contrasted to classical (Lorentz-model) dynamics, such as quantum saturation. In the context of a diagonalized atom-photon Hamiltonian, we discuss inversion, dressed states, and light shifts. Applications of this foundational material include electromagnetically induced transparency, slow light, dark states, and laser cooling.

This course will examine the physics of the quantum electromagnetic field, and its interaction with other quantum mechanical objects. The broad purpose of the course is to equip students with the tools and background needed to connect with current research in quantum optics. Outline of topics: Quantization of the electromagnetic field; Quantum Coherence Theory; Representation of Quantum States; Squeezed Light; Master Equations; Light Matter Interactions.