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- Title
Markovian repeated interaction quantum systems.
- Authors
Bougron, Jean-François; Joye, Alain; Pillet, Claude-Alain
- Abstract
We study a class of dynamical semigroups ( n) n ∈ ℕ that emerge, by a Feynman–Kac type formalism, from a random quantum dynamical system (ℒ ω n ∘ ⋯ ∘ ℒ ω 1 (ρ ω 0 )) n ∈ ℕ driven by a Markov chain (ω n) n ∈ 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 . As a physical application, we consider the case where the ℒ ω 's are the reduced dynamical maps describing the repeated interactions of a system with thermal probes ℰ ω . 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.
- Subjects
RANDOM dynamical systems; NONEQUILIBRIUM statistical mechanics; MARKOV processes; ENTROPY
- Publication
Reviews in Mathematical Physics, 2022, Vol 34, Issue 9, p1
- ISSN
0129-055X
- Publication type
Article
- DOI
10.1142/S0129055X22500283