Markovian Repeated Interaction Quantum Systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866929511209107456 |
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| author | Bougron, Jean-François Joye, Alain Pillet, Claude-Alain |
| author_facet | Bougron, Jean-François Joye, Alain Pillet, Claude-Alain |
| contents | 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 $(\mathcal{L}_{ω_n}\circ\cdots\circ\mathcal{L}_{ω_1}(ρ_{ω_0}))_{n\in\mathbb{N}}$ driven by a Markov chain $(ω_n)_{n\in\mathbb{N}}$. 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 $\mathcal{L}_ω$'s are the reduced dynamical maps describing the repeated interactions of a system $\mathcal{S}$ with thermal probes $\mathcal{C}_ω$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_05321 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Markovian Repeated Interaction Quantum Systems Bougron, Jean-François Joye, Alain Pillet, Claude-Alain Mathematical Physics Statistical Mechanics Quantum Physics 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 $(\mathcal{L}_{ω_n}\circ\cdots\circ\mathcal{L}_{ω_1}(ρ_{ω_0}))_{n\in\mathbb{N}}$ driven by a Markov chain $(ω_n)_{n\in\mathbb{N}}$. 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 $\mathcal{L}_ω$'s are the reduced dynamical maps describing the repeated interactions of a system $\mathcal{S}$ with thermal probes $\mathcal{C}_ω$. 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. |
| title | Markovian Repeated Interaction Quantum Systems |
| topic | Mathematical Physics Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2202.05321 |