# Graduate Courses

## Current Course Offerings

are listed here.

## Graduate Course Descriptions

### 6000 Condensed Matter Physics I

Crystal lattices and reciprocal lattices, electronic states, lattice vibrations and elastic waves, and thermal properties of solids.

### 6001 Condensed Matter Physics II

A study of quantum excitations in solids; phonons, magnons, plasmons and excitons; the coulomb gas and fermi liquid theory; the BCS theory of superconductivity and the thermodynamic properties of superconductors.

### 6002 Theory of Superconductivity

The phenomena of superconductivity, the Cooper pair problem, BCS theory, the electron-phonon interaction and the Eliashberg theory of strong coupling superconductors.

### 6003 Path Integral Techniques in Condensed Matter Physics

An introduction to path integrals and their application to problems in condensed matter physics. Specific topics include: Brownian motion, macromolecules, path integral formulation of quantum mechanics and classical and quantum statistical physics.

### 6012 Advanced Photonics

A study on the principles of light, light propagation, lasers, and the properties of photonic materials, devices, and systems as well as their applications in optical signal processing, optical communication, and optical sensing.

### 6040 Biophysics

Biophysics is focused on the physics of biologically important processes. It includes an introduction to biological molecules and cell physiology. It deals with biologically-relevant aspects of thermal physics and statistical mechanics including diffusion, random walk, viscosity and low Reynold's number conditions, entropy and free energy and entropic forces. Other topics include self-assembly and cooperative transitions in the context of membranes, macromolecules and protein folding and the kinetics of molecular machines and enzymes. This course is intended for students with a background in physical science but not necessarily in life science.

### 6200 Nonlinear Dynamics

Nonlinear ordinary differential equations, bifurcation theory, nonlinear maps, chaos, nonlinear partial differential equations, stability analysis, pattern formation, spatiotemporal dynamics.

### 6308 Ocean Dynamics I

The physics of ocean waves and tides; theory of surface and internal waves, windwave spectra, theory and analysis of the astronomical tides, seiches and co-oscillations.

### 6309 Ocean Dynamics II

Basic equations of ocean dynamics; geostrophic, gradient and inertial, Ekman, baroclinic, and barotropic flows; theories of ocean circulation.

### 6310 Physical Oceanography

Introductory physical oceanography, the physical nature of the oceans, physical properties of sea water and sea ice; ocean current systems, water masses, waves, tides, selected topics.

### 6313 Physical Fluid Dynamics

Stress, vorticity, rate of strain and deformation, Navier-Stokes equations, Bernoulli's and Kelvin's theorems, incompressibility and Boussinesq approximations, potential flow, waves, KdV equation, compressible flow, Reynolds number, boundary layers, flow around bluff bodies and aerofoils.

### 6316 Ocean Measurements and Data Analysis

Measurement principles, limitations of sensors, design of field programs, time-series analysis methods, application of these methods to oceanographic data.

### 6317 Ocean Acoustics

Fundamentals of sound propagation and scattering in the ocean: the equations governing the acoustic field in homogeneous fluid and elastic media; complex dispersion relations; reflection and refraction at an interface; sound scattering and absorption; phase shifts; resonance scattering; sound propagation in randomly varying inhomogeneous media.

### 6318 Numerical Modeling

Finite difference techniques, computational dispersion, stability of numerical techniques, elliptic solvers, spectral models, tidal models, shelf circulation models, ocean general circulation models, climate models, data assimilation.

### 6319 Climate Dynamics

Thermohaline convection: observations and theory; ocean climate models; surface boundary conditions, coupled ocean-atmosphere models; box models; variability on interdecadal, century and geological time scales; global warming.

### 6321 Coastal Oceanography

Coastal circulation: observations and theory; coastal trapped waves; wind-forced response; tides; uniform density models; effect of density stratification; interaction with large scale ocean circulation; numerical modeling of coastal circulation; fisheries applications.

### 6322 Stratified Fluids

Internal waves, Garrett and Munk spectrum, nonlinear interactions. Wave generation: flow over topography and atmospheric forcing. Gravity currents, internal tides, weakly nonlinear theory, solitary waves, turbulence, influence of stratification on wakes.

### 6320 Turbulence

Basic conservation equations for homogeneous and inhomogeneous turbulent flow, locally isotropic turbulence and the Kolmogorov theory, spectral theory, turbulent boundary layers, entrainment and mixing in stratified shear flow.

### 6323 Stability Theory

Kelvin-Helmholtz and Rayleigh-Taylor instabilities, centrifugal instability, stability on *f* and β planes. Effects of viscosity: Orr-Sommerfeld equation. Thermal instability, stability of stratified fluids, baroclinic instability, transition to turbulence.

### 6400 Statistical Mechanics

Microcanonical, canonical and grand canonical ensembles in classical statistical mechanics, partition function and Helmholtz free energy, derivation of thermodynamic quantities, postulates of quantum statistical mechanics, density matrix, canonical and grand canonical quantum distributions, applications of Fermi-Dirac and Bose-Einstein statistics, statistical mechanics of interacting systems.

### 6402 Theory of Phase Transitions

Thermodynamic description and statistical mechanics of phase transitions and critical phenomena. Landau theory and the classical description of phase transitions. Fluctuations and the breakdown of Landau theory. Phenomenological scaling theory in static and dynamic critical phenomena. Renormalisation group and critical phenomena. Continuous symmetry. Critical phenomena near four dimensions.

### 6403 Stochastic Processes, Time-dependent and Nonequilibrium Statistical Mechanics

Transport processes, random walk theory, Brownian motion; stochastic processes; time series, stationarity, autocorrelation, and power spectra; Gaussian processes, Markov processes, the Wiener process, the Ornstein-Uhlenbeck process; the Master Equation and the Fokker-Planck equation; derivation and elementary properties of the Boltzmann equation.

### 6502 Electrodynamics

Maxwell's equations, special relativity and electrodynamics, electrodynamics of continuous media, electromagnetic wave propagation, diffraction, waveguides and cavities, radiation from a localized oscillator.

### 6720 Introductory Theory of Molecules

Diatomic molecules; molecular orbital theory, hydrogen molecular ion, hydrogen molecule, intermolecular forces, Born-Oppenheimer approximation, vibration-rotation, LCAO/MO and SCF wave functions, electronic energy levels and transitions. Polyatomic molecules; classification, rotation and vibration symmetries and wave functions, group theory.

### 6721 Molecular Spectroscopy

Spectra of diatomic molecules; rigid and non-rigid rotators, harmonic and anharmonic oscillators, symmetric top model, statistical weights and intensities, vibrational structure of electronic transitions, isotopic effects, Franck-Condon principle and intensities, classification of electronic states, Hund's coupling cases, rotational structure of electronic bands. Infrared and Raman spectra: polarizability and electric moments, selection rules. Brillouin scattering.

### 6722 Light Scattering Spectroscopy

Historical perspective; Raman scattering --- theory, experimental techniques, detailed discussion and interpretation of selected experiments; Brillouin scattering --- theory, experimental techniques, detailed discussion and interpretation of selected experiments; comparison with Raman/Brillouin gain techniques; Rayleigh scattering (optional) -- theory, experimental techniques, discussion and interpretation of selected experiments.

### 6730 Molecular Theory of Liquids and Compressed Gases

Thermal properties of liquids, orientation and rotational motion of molecules in liquids, surface and allied phenomena; thermal properties of gases, the second virial coefficient, intermolecular forces.

### 6740 Physics of Atomic Collisions

Selected topics in atomic and molecular scattering. Electron collisions with atoms. General and semi-empirical theories of elastic and inelastic scattering. Methods of approximation in e-atom collisions. Ionization. Analytical theory of scattering for slow collisions. Collisions with ions.

### 6800 Group Theory

Abstract group theory, theory of group representations, physical applications of group theory to problems in condensed matter physics and atomic and molecular physics.

### 6850 Quantum Mechanics I

Vectors and operators, matrix representation of vectors and operators, transformations; general formalism of quantum theory; identical particles, perturbation theories, angular momentum, collision theory.

### 6851 Quantum Mechanics II

Advanced treatment of angular momentum, formal theory of scattering, relativistic dynamical equations, field theory.

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