Weak-Memory Dynamics in Discrete Time
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917554113478656 |
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| author | Meyer, Hugues Brandner, Kay |
| author_facet | Meyer, Hugues Brandner, Kay |
| contents | Discrete dynamics arise naturally in systems with broken temporal translation symmetry and are typically described by first-order recurrence relations representing classical or quantum Markov chains. When memory effects induced by hidden degrees of freedom are relevant, however, higher-order discrete evolution equations are generally required. Focusing on linear dynamics, we identify a well-delineated weak-memory regime where such equations can, on an intermediate time scale, be systematically reduced to a unique first-order counterpart acting on the same state space. We formulate our results as a mathematical theorem and work out two examples showing how they can be applied to stochastic Floquet dynamics under coarse-grained and quantum collisional models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak-Memory Dynamics in Discrete Time Meyer, Hugues Brandner, Kay Statistical Mechanics Mesoscale and Nanoscale Physics Quantum Physics Discrete dynamics arise naturally in systems with broken temporal translation symmetry and are typically described by first-order recurrence relations representing classical or quantum Markov chains. When memory effects induced by hidden degrees of freedom are relevant, however, higher-order discrete evolution equations are generally required. Focusing on linear dynamics, we identify a well-delineated weak-memory regime where such equations can, on an intermediate time scale, be systematically reduced to a unique first-order counterpart acting on the same state space. We formulate our results as a mathematical theorem and work out two examples showing how they can be applied to stochastic Floquet dynamics under coarse-grained and quantum collisional models. |
| title | Weak-Memory Dynamics in Discrete Time |
| topic | Statistical Mechanics Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2510.26325 |