Open Quantum Systems Theory

Introduction to Markovian master equations: the Redfield equation, the secular master equation, and the Caldeira–Leggett master equation. Collision models and the singular-coupling master equation. Regularization of the Redfield equation and positivity. Introduction to the Keldysh formalism. Introduction to path integrals and the Feynman-Vernon influence functional. Tunneling and the semiclassical limit. Keldysh rotation and the classical limit. Introduction to Green’s functions in open quantum systems. Introduction to non-Markovian approaches: the Nakajima-Zwanzig projection operator technique and the time-convolutionless master equation. Stochastic non-Markovian equations: the quantum Langevin equation, the two-state unraveling, quantum state diffusion, and the stochastic Liouville-von Neumann equation. Exact Gaussian non-Markovian equations: the Hu-Paz-Zhang master equation and the Gaussian Master Equation. Introduction to thermodynamics and transport in open quantum systems theory: full counting statistics techniques and two-point measurement schemes. First and second law of thermodynamics: the fluctuation theorem, the Jarzynski equality and the notion of detailed balance. Aspects of work: passive states and quantum ergotropy. Optimization problems in open quantum systems theory: introduction to semidefinite programming. Distinguishability of quantum states and quantum channels. Moment-matrix approaches for quantum many-body systems. Basic notions of continuous monitoring: homodyne, heterodyne, and photodetection stochastic master equations.