Nonequilibrium Statistical Physics

STOCHASTIC PROCESSES
- Realizations and probabilities
- Reduced probabilities, examples
- Markov process and master equation
- One-step processes and random walk
- Continuous time limit and master equation
- Example: Radioactive decay
- Wiener process Telegraph equation and Poisson process
BROWNIAN MOTION
- Langevin Equation
- Spectral density and autocorrelation function Fokker Planck equation
- Application to Brownian motion
DYNAMICAL SYSTEMS
- Hamiltonian systems
- Distribution function
- The statistical operator
- Equations of motion for statistical operator/ distribution function
- Classical reduced distribution functions
- Quantum statistical reduced distribution functions
- Equations of motion for reduced distribution functions
DERIVATION OF A NONEQUILIBRIUM STATISTICAL OPERATOR
- Equation of motion and boundary conditions
- Thermal equilibrium The relevant statistical operator
- Statistical operator for the nonequilibrium
- Projection operator and statistical operator for the nonequilibrium
- Example: Scattering theory
QUANTUM MASTER EQUATION
- Open systems interacting with a bath
- Derivation of the quantum master equation
- Born-Markov and rotating wave approximation
- Example: Atom coupled to the electromagnetic field
- Further examples for the quantum master equation
- The quantum Fokker-Planck equation
- The classical limit
KINTEIC EQUATIONS
- The Boltzmann equation
- Derivation from the nonequilibrium statistical operator
- Properties of the Boltzmann equation, improvements
- The linearized Boltzmann equation
- The hydrodynamical equations
- Relaxation time method
- The Kohler variational principle
- The Vlasov-Landau equation
LINEAR RESPONSE THEORY AND FLUCTUATION-DISSIPATION THEOREM
- Transport phenomena and thermodynamics of irreversible processes
- Non-equilibrium statistical operator and linear response
- Example: Conductivity of a plasma
- Improved linear response

Prof. Dr. Gerd Roepke is professor of Theoretical Physics at the University of Rostock, Germamy. Having obtained his academic degrees from the University of Leipzig, he spent most of his career working at the Technical University Dresden before the appointment at Rostock. Professor Roepke has authored over 300 scientific publications on quantum statistics, nonequilibrium statistical mechanics, plasma physics and nuclear theory, including several monographs, and received different awards. He is a member of the Saxonian Academy of Sciences and external member of the Max-Planck Society.