Markovian Repeated Interaction Quantum Systems

• URL: http://arxiv.org/abs/2202.05321v1
• Date: Thu, 10 Feb 2022 20:52:40 GMT
• Title: Markovian Repeated Interaction Quantum Systems
• Authors: Jean-Fran\c{c}ois Bougron and Alain Joye and Claude-Alain Pillet
• Abstract summary: We study a class of dynamical semigroups $(mathbbLn)_ninmathbbN$ that emerge, by a Feynman--Kac type formalism, from a random quantum dynamical system. As a physical application, we consider the case where the $mathcalL_omega$'s are the reduced dynamical maps describing the repeated interactions of a system with thermal probes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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