Quantum collision models: open system dynamics from repeated interactions

TL;DR

This paper provides a comprehensive, pedagogical overview of quantum collision models, highlighting their definitions, properties, and applications in open quantum systems, including derivations of master equations and non-Markovian dynamics.

Contribution

It offers an extensive, accessible introduction to quantum collision models, connecting them with various aspects of open quantum systems and recent research developments.

Findings

Clarifies the role of collision models in deriving master equations

Explores non-Markovian extensions of collision models

Links collision models with input-output formalism and quantum thermodynamics

Abstract

We present an extensive introduction to quantum collision models (CMs), also known as repeated interactions schemes: a class of microscopic system-bath models for investigating open quantum systems dynamics whose use is currently spreading in a number of research areas. Through dedicated sections and a pedagogical approach, we discuss the CMs definition and general properties, their use for the derivation of master equations, their connection with quantum trajectories, their application in non-equilibrium quantum thermodynamics, their non-Markovian generalizations, their emergence from conventional system-bath microscopic models and link to the input-output formalism. The state of the art of each involved research area is reviewed through dedicated sections. The article is supported by several complementary appendices, which review standard concepts/tools of open quantum systems used in the main text with the goal of making the material accessible even to readers possessing only a basic background in quantum mechanics. The paper could also be seen itself as a friendly, physically intuitive, introduction to fundamentals of open quantum systems theory since most main concepts of this are treated such as quantum maps, Lindblad master equation, steady states, POVMs, quantum trajectories and stochastic Schrodinger equation.