A perturbation theory for multi-time correlation functions in open quantum systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916929190494208 |
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| author | Szańkowski, Piotr |
| author_facet | Szańkowski, Piotr |
| contents | Dynamical maps are the principal subject of the open system theory. Formally, the dynamical map of a given open quantum system is a density matrix transformation that takes any initial state and sends it to the state at a later time. Physically, it encapsulates the system's evolution due to coupling with its environment. Hence, the theory provides a flexible and accurate framework for computing expectation values of open system observables. However, expectation values -- or more generally, single-time correlation functions -- capture only the simplest aspects of a quantum system's dynamics. A complete characterization of the dynamics requires access to multi-time correlation functions as well: phenomena like detailed balance, linear and non-linear response, non-equilibrium transport in general, or even sequential measurements of system observables are all described in terms of multi-time correlations. For closed systems, such correlations are well-defined, even though knowledge of the system's state alone is insufficient to determine them fully. In contrast, the standard dynamical map formalism for open systems does not account for multi-time correlations, as it is fundamentally limited to describing state evolution. Here, we extend the scope of open quantum system theory by developing a systematic perturbation theory for computing multi-time correlation functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A perturbation theory for multi-time correlation functions in open quantum systems Szańkowski, Piotr Quantum Physics Dynamical maps are the principal subject of the open system theory. Formally, the dynamical map of a given open quantum system is a density matrix transformation that takes any initial state and sends it to the state at a later time. Physically, it encapsulates the system's evolution due to coupling with its environment. Hence, the theory provides a flexible and accurate framework for computing expectation values of open system observables. However, expectation values -- or more generally, single-time correlation functions -- capture only the simplest aspects of a quantum system's dynamics. A complete characterization of the dynamics requires access to multi-time correlation functions as well: phenomena like detailed balance, linear and non-linear response, non-equilibrium transport in general, or even sequential measurements of system observables are all described in terms of multi-time correlations. For closed systems, such correlations are well-defined, even though knowledge of the system's state alone is insufficient to determine them fully. In contrast, the standard dynamical map formalism for open systems does not account for multi-time correlations, as it is fundamentally limited to describing state evolution. Here, we extend the scope of open quantum system theory by developing a systematic perturbation theory for computing multi-time correlation functions. |
| title | A perturbation theory for multi-time correlation functions in open quantum systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.19137 |