Repeated interactions in open quantum systems

Abstract

Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the dynamics of quantum coherences (decoherence) and quantum correlations (entanglement), or the emergence of heat and particle fluxes in non-equilibrium situations. From the mathematical physics perspective, one of the main challenges is to derive the irreversible dynamics of the open system, starting from a unitary dynamics of the system and its environment. The repeated interactions systems considered in these notes are models of non-equilibrium quantum statistical mechanics. They are relevant in quantum optics, and more generally, serve as a relatively well treatable approximation of a more difficult quantum dynamics. In particular, the repeated interaction models allow to determine the large time (stationary) asymptotics of quantum systems out of equilibrium.

Lecture notes of the summer school "Non-equilibrium statistical mechanics" (Montreal, July 2011)

References in corpus (9)

• Quantum walks: a comprehensive review
• Asymptotic evolution of quantum walks with random coin
• Existence, uniqueness and approximation of a stochastic Schrödinger equation: the diffusive case
• Theory of Non-Equilibrium Sationary States as a Theory of Resonances
• Repeated quantum non-demolition measurements: convergence and continuous-time limit
• Random repeated interaction quantum systems
• The effect of time-dependent coupling on non-equilibrium steady states
• Non-equilibrium states of a photon cavity pumped by an atomic beam
• Repeated Interaction Quantum Systems: van Hove Limits and Asymptotic States

Cited by in corpus (43)

• Quantum collision models: open system dynamics from repeated interactions
• Entropy accumulation
• Quantum speed-up in collisional battery charging
• Open quantum system dynamics and the mean force Gibbs state
• Collision models can efficiently simulate any multipartite Markovian quantum dynamics
• Apparent temperature: demystifying the relation between quantum coherence, correlations, and heat flows
• Open dynamics under rapid repeated interaction
• Irreducible decompositions and stationary states of quantum channels
• Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states
• Landauer's Principle in Repeated Interaction Systems
• A steady state quantum classifier
• Quantum master equations for entangled qubit environments
• The Unruh effect in slow motion
• On entropy production of repeated quantum measurements II. Examples
• Multipartite correlations in quantum collision models
• An ergodic theorem for quantum processes with applications to matrix product states
• Theory of Ergodic Quantum Processes
• A note on the Landauer principle in quantum statistical mechanics
• Perturbation Analysis of Quantum Reset Models
• Concentration Inequalities for Output Statistics of Quantum Markov Processes
• Landauer's Principle for Trajectories of Repeated Interaction Systems
• Almost thermal operations: inhomogeneous reservoirs
• Linear response theory and entropic fluctuations in repeated interaction quantum systems
• An Extension of ETH to Non-Equilibrium Steady States
• Purification in Rapid Repeated Interaction Systems
• Dynamics of an Open System for Repeated Harmonic Perturbation
• Markovian Repeated Interaction Quantum Systems
• Dynamical Semigroups for Unbounded Repeated Perturbation of Open System
• On Fermionic walkers interacting with a correlated structured environment
• Thermalization of Fermionic Quantum Walkers
• Unified Collision Model of Coherent and Measurement-based Quantum Feedback
• Queued quantum collision models
• Thermal state preparation by repeated interactions at and beyond the Lindblad limit
• Fermionic walkers driven out of equilibrium
• Collisional-model quantum trajectories for entangled qubit environments
• Quantum Measurements of Scattered Particles
• Simulating quantum collision models with Hamiltonian simulations using early fault-tolerant quantum computers
• Entropy Production of Quantum Reset Models
• Thermal Contact: Mischief and Time Scales
• Violation of the thermodynamic uncertainty relation in quantum collisional models
• A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement
• Rigorous results on approach to thermal equilibrium, entanglement, and nonclassicality of an optical quantum field mode scattering from the elements of a non-equilibrium quantum reservoir
• Quantum Statistical Mechanics of Electronically Open Molecules: Reduced Density Operators