Graduate Program Courses
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.
6040 Biophysics
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.