Overview

1. `Simple' Systems with few degrees of freedom: typically quantum optics systems, atoms, few-level systems, cavity modes.

• Weak coupling approximation: Master Equation (Born and Markov Approximation)
• Damped harmonic oscillator.
• Solution methods: phase-space methods ($P$-representation etc.).
• Solution methods: quantum trajectories.
• Correlation Functions, Quantum Regression Theorem.
• Beyond weak coupling approximation: Feynman-Vernon influence functional (path integral) theories; R. P. Feynman, F. L. Vernon, Ann. Phys. (N.Y.) 24, 118 (1963). Non-exponential decay laws at low temperatures.
• Exact solution of damped harmonic oscillator.
• Spin-Boson Problem, Two-Level System.
• Non-Markovian versus Markovian, Lindblad versus non-Lindblad.
• `Non-standard' methods.

2. Systems with many degrees of freedom: typically condensed matter systems, electrons + phonons (particle statistics).

• Quasiclassical kinetic theories, Boltzmann equation.
• Quantum Many-Body Non-Equilibrium Methods. (Keldysh) Greens Function Methods, quantum Boltzmann equation.

In this chapter, we will concentrate on 1. (`Simple' Systems with few degrees of freedom). Also, not discussed in detail in this lecture are

• Nakajima-Zwanzig theories, Mori projection operator theories. These give a more formal approach towards system-bath theories.
• `Early approaches' such as Wigner-Weisskopf theory of spontaneous emission.
• ...

Generally speaking, quantum dissipation can be regarded as a subfield of non-equilibrium quantum statistics/ non-equilibrium many-body theory.