Content

Fluctuation around equilibrium. Non-equilibrium thermodynamics, transport coefficients, Onsager relations.
Time evolution of classical non-equilibrium systems: Liouville equation and master equation.
Boltzmann equation and time irreversibility. Scattering integrals for particle-impurity and particle-particle scattering. Local equilibrium, hierarchy of relaxation times.
Hydrodynamics and diffusion.
Applications of Boltzmann equation to transport theory.
Macroscopic particle in an environment. Langevin equation, and Fokker-Planck equation. Nyquist noise in electrical circuits. Spectral theory for fluctuations, fluctuation-dissipation relation.
Principles of quantum statistics. Density matrix for simple quantum systems. Evolution of non-equilibrium quantum systems: relaxation and dephasing.
Pauli master equation. Quantum kinetics of two-level systems. Kinetic equation in quantum optics.
Linear response theory, and quantum fluctuation-dissipation theorem.

Course material

L. E. Reichl, "A Modern Course in Statistical Physics" (Wiley, NY, 1998).
Lecture notes.

Format: more information

After having taken "Statistical Physics" the student should have acquired:

• knowledge of the basic concepts and methods of the kinetic theory for classical and quantum many body systems
• understanding the origin of irreversible evolution of physical, chemical, and biological systems, and hierarchy of relaxation processes
• practical skills in solving transport problems, analyzing fluctuation phenomena, and noise.