Phase diagrams. Critical phenomena and universal scaling. Mean field and Landau theories. Kadanoff scaling theory. Position space and momentum space renormalization. Chaotic renormalization groups and spin-glass order. Quenched disordered and frustrated systems. Phase diagrams of quantum spin and electronic conductivity models.
Interaction of electromagnetic radiation with atoms and molecules, rotational spectroscopy, vibrational spectroscopy, electronic spectroscopy, spectroscopic instrumentation, lasers as spectroscopic light sources, fundamentals of lasers, nonlinear optical spectroscopy, laser Raman spectroscopy.
Free electron theory of metals. Crystal lattices. Reciprocal lattice. Classification of Bravais lattices. X-ray diffraction and the determination of crystal structures. Electrons in a periodic potential. Tight binding method. Band structures. Semi-classical theory of conduction in metals. Fermi surface. Surface effects.
Classification of solids. Theory of harmonic crystals. Phonons and phonon dispersion relations. Anharmonic effects in crystals. Phonons in metals. Dielectric properties of insulators. Semiconductors. Diamagnetism and paramagnetism. Electron interactions and magnetic structure. Magnetic ordering. Superconductivity.
Linear algebra: Vector and inner product spaces, linear operators, eigenvalue problems; Vector calculus: Review of differential and integral calculus, divergence and Stokes' theorems. Ordinary differential equations: Linear equations, Sturm-Liouville theory and orthogonal functions, system of linear equations; Methods of mathematics for science and engineering students.
Computational modeling of scientific problems and implementation of the numerical methods. Dynamical systems based on ordinary differential equations, nonlinear dynamics and chaos, potentials and fields, random systems, statistical mechanics, phase transitions, molecular dynamics, computational quantum mechanics, interdisciplinary topics such as protein folding, self-organized criticality, genetic algorithms.
Lorentz transformations and Minkowski space-time. Tensors and spinors. Variational formulation of relativistic wave equations. Noether theorem: Symmetries and conservation laws.
Basic differential geometric concepts. Space-time metric and connection. Curvature and torsion tensors. Einstein field equations. Gravitational waves. Black holes. Big bang cosmologies.
Quantization of free fields. Propagators. Interacting fields and the S-matrix. Loop expansion of the S-matrix and Feynman diagrams. Path integral techniques. QED. Radiative corrections. Renormalization. Effective field theories.
Introduction to non-Abelian gauge field theories. QCD. Spontaneous symmetry breakdown and mass generation. Standard model of electroweak interactions. Non-perturbative effects. Supersymmetry.
Invariances of the Schrödinger equation. Conservation laws and spectrum degeneracies. Parity and time-reversal symmetries. Translation symmetries on lattices. Crystallographic space groups. SO(3) rotation group. Unitary transformations. Symmetries in nuclear and elementary particle physics. SU(2) and isospin. SU(3) and strangeness.
Optical micro-cavities. Fabry-Perot cavity. Quality factor. Finesse. Free-spectral bands. Whispering gallery modes. Coupling. Photonic molecules, glasses, crystals and meta-materials. Optical micro-cavities. Fabry-Perot cavity. Quality factor. Finesse. Free-spectral bands. Whispering gallery modes. Coupling. Photonic molecules, glasses, crystals and meta-materials.
Review of electromagnetism; geometrical optics, analysis of optical systems; wave properties of light, Gaussian beams, beam optics; interaction of light with matter, spontaneous and stimulated emission, optical amplification, theory and applications of lasers, optical interactions in semiconductors, light emitting diodes and diode lasers; detectors, noise in detection systems; light propagation in anisotropic crystals, Pockels and Kerr effect, light modulators; nonlinear optics, second harmonic generation, phase matching, nonlinear optical materials.
Quantized atomic models. Spectroscopy. Light-atom interactions. Radiative transitions. Atom-atom interactions. Magnetic interactions of atoms. Molecular structure. Multi-electron systems. Trapping ions or atoms. Atom optics. Bose-Einstein condensation. Atomic chips. Quantum computation by matter waves and trapped ions.
Quantum theory of light. Coherent light. Non-classical states of light. Quantum interferometry. Quantum measurements. Interaction of light with matter. Cavity quantum electrodynamics. Quantum entanglement and quantum teleportation. Non-linear optics. Photonic band gaps. Quantum information theory and the fundamental principles of quantum computation.
Principles of optical microscopes. Microscopy methods. Photo-physics of dye molecules. Exciting fluorescence and its observation. Dipole radiation near planar interfaces. Photon-counting analysis. Flourescence correlation spectroscopy. Flourescence resonance energy transfer (FRET). Optical spectroscopy at low temperatures. Semiconducting nano-crystals. Metallic nano-particles.
Survey of the properties and applications of photonic materials and devices; semiconductors; photon detectors, light emitting diodes, noise in light detection systems; light propagation in anisotropic media, Pockels and Kerr effects, light modulators, electromagnetic wave propagation in dielectric waveguides, waveguide dispersion; nonlinear optical materials, second harmonic generation, Raman converters.
Survey of the techniques for the generation of picosecond and femtosecond pulses from lasers; active and passive mode locking, saturable absorbers, master equation, theory of Kerr lens mode locking; propagation of ultrashort pulses in nonlinear and dispersive media; Measurement and characterization of ultrashort pulses; applications of femtosecond lasers in spectroscopy, medicine, and industry.
Random walk problems and probability concepts. Theory of polymers. Statistical mechanical concepts with emphasois on self-avoiding walks and biological polymer models: ensembles, free energy, entropy, scaling. Lattices as interacting models of random systems and phase transitions. Dynamical phenomena: Master equation (Examples: random walk and lattice growth), Langevin equation and its generalizations. Chaos and order.
Provides hands-on teaching experience to graduate students in undergraduate courses. Reinforces students' understanding of basic concepts and allows them to communicate and apply their knowledge of the subject matter.