Markovian Repeated Interaction Quantum Systems

Abstract

We study a class of dynamical semigroups $({\mathbb{L}}^n{)}_{n\in \mathbb{N}}$ that emerge, by a Feynman--Kac type formalism, from a random quantum dynamical system $({\mathcal{L}}_{{\omega }_n}\circ \cdots \circ {\mathcal{L}}_{{\omega }_1}({\rho }_{{\omega }_0}){)}_{n\in \mathbb{N}}$ driven by a Markov chain $({\omega }_n{)}_{n\in \mathbb{N}}$. We show that the almost sure large time behavior of the system can be extracted from the large $n$ asymptotics of the semigroup, which is in turn directly related to the spectral properties of the generator $\mathbb{L}$. As a physical application, we consider the case where the ${\mathcal{L}}_{\omega }$'s are the reduced dynamical maps describing the repeated interactions of a system $\mathcal{S}$ with thermal probes ${\mathcal{C}}_{\omega }$. We study the full statistics of the entropy in this system and derive a fluctuation theorem for the heat exchanges and the associated linear response formulas.

References in corpus (37)

• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Dynamical ensembles in stationary states
• Fluctuation theorems: Work is not an observable
• An improved Landauer Principle with finite-size corrections
• Chaotic hypothesis: Extension of Onsager reciprocity to large fields and the chaotic hypothesis
• Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
• Quantum Fluctuation Relations for the Lindblad Master Equation
• Repeated interactions in open quantum systems
• A Pathwise Ergodic Theorem for Quantum Trajectories
• Fluctuations of Quantum Currents and Unravelings of Master Equations
• Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems
• Entropic fluctuations of quantum dynamical semigroups
• On entropy production of repeated quantum measurements I. General theory
• Homogeneous Open Quantum Random Walks on a lattice
• Steady state fluctuations of the dissipated heat for a quantum stochastic model
• Entropic fluctuations in thermally driven harmonic networks
• Landauer's Principle in Repeated Interaction Systems
• Random repeated interaction quantum systems
• Random repeated quantum interactions and random invariant states
• Diffusion of wave packets in a Markov random potential
• On entropy production of repeated quantum measurements II. Examples
• Repeated and continuous interactions in open quantum systems
• Entropic fluctuations in XY chains and reflectionless Jacobi matrices
• Large Deviations and Fluctuation Theorem for Selectively Decoupled Measures on Shift Spaces
• A note on the Landauer principle in quantum statistical mechanics
• Scattering induced current in a tight-binding band
• Landauer's Principle for Trajectories of Repeated Interaction Systems
• Full statistics of energy conservation in two times measurement protocols
• Mixing properties of the one-atom maser
• Linear response theory and entropic fluctuations in repeated interaction quantum systems
• Control of fluctuations and heavy tails for heat variation in the two-time measurement framework
• On Fermionic walkers interacting with a correlated structured environment
• Thermalization of Fermionic Quantum Walkers
• A Detailed Fluctuation Theorem for Heat Fluxes in Harmonic Networks out of Thermal Equilibrium
• Fermionic walkers driven out of equilibrium

Cited by in corpus (4)

• Entropy Production of Quantum Reset Models
• Quenched large deviations of Birkhoff sums along random quantum measurements
• A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement
• Asymptotic Purification of Quantum Trajectories under Random Generalized Measurements