Lidar Daniel A. Lecture Notes on the Theory of Open Quantum Systems

Departments of Electrical Engineering, Chemistry, and Physics & Astronomy. Center for Quantum Information Science & Technology. University of Southern California, arXiv.org, 2019. — 131 p.This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations, both Markovian and non-Markovian.
Inside...
Review of Quantum Mechanics.
Density Operators.
Composite Systems.
Open System Dynamics.
Complete Positivity and Quantum Maps.
Quantum Maps of a Qubit.
Quantum Maps from First Principles.
Derivation of the Lindblad equation from a short time expansion of quantum maps.
The Lindblad equation via coarse graining.
Analytical solution of the spin-boson model for phase damping.
Quantum trajectories and unravelling the Lindblad equation.
Analytical solution of the general Lindblad equation.
Derivation of the Lindblad equation from the cumulant expansion and coarse graining.
First-principles derivation of the Lindblad equation from the Born, Markov, and rotating wave approximations.
The Kubo-Martin-Schwinger (KMS) condition and the Gibbs state as a stationary state Lindblad equation.
Pauli Master Equation.
Lindblad Equation in the Singular Coupling Limit.
The Nakajima-Zwanzig Equation.
The Time Convolutionless Master Equation.
Post Markovian Master Equation...