Nonequilibrium steady state in Lindblad dynamics for infinite quantum spin systems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916890500136960 |
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| author | Shimomura, Kenji Hara, Nagisa Kusuoka, Seiichiro |
| author_facet | Shimomura, Kenji Hara, Nagisa Kusuoka, Seiichiro |
| contents | We consider Lindblad dynamics of quantum spin systems on infinite lattices and define a nonequilibrium steady state (NESS) and a time-averaged nonequilibrium steady state (TANESS) on the basis of $C^*$-algebraic formalism. Generically, the NESS on an infinite system does not equal the thermodynamic limit of NESSs on finite systems. We give a sufficient condition that they coincide with each other, in terms of both a condition number, which quantifies the normality of a Liouvillian, and some spectral gaps on finite subsystems. To appreciate the importance of the condition number, we provide an example in which the spectral gaps have nonzero lower bounds uniformly for any finite subsystems but a thermodynamic limit and a long-time limit (or a long-time average) do not commute with each other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07448 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonequilibrium steady state in Lindblad dynamics for infinite quantum spin systems Shimomura, Kenji Hara, Nagisa Kusuoka, Seiichiro Mathematical Physics Statistical Mechanics Strongly Correlated Electrons Quantum Physics We consider Lindblad dynamics of quantum spin systems on infinite lattices and define a nonequilibrium steady state (NESS) and a time-averaged nonequilibrium steady state (TANESS) on the basis of $C^*$-algebraic formalism. Generically, the NESS on an infinite system does not equal the thermodynamic limit of NESSs on finite systems. We give a sufficient condition that they coincide with each other, in terms of both a condition number, which quantifies the normality of a Liouvillian, and some spectral gaps on finite subsystems. To appreciate the importance of the condition number, we provide an example in which the spectral gaps have nonzero lower bounds uniformly for any finite subsystems but a thermodynamic limit and a long-time limit (or a long-time average) do not commute with each other. |
| title | Nonequilibrium steady state in Lindblad dynamics for infinite quantum spin systems |
| topic | Mathematical Physics Statistical Mechanics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2508.07448 |