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.

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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