Temperature and conditions for thermalization after canonical quenches
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912706336915456 |
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| author | Dabelow, Lennart |
| author_facet | Dabelow, Lennart |
| contents | We consider quenches of a quantum system that is prepared in a canonical equilibrium state of one Hamiltonian and then evolves unitarily in time under a different Hamiltonian. Technically, our main result is a systematic expansion of the pre- and post-quench canonical ensembles in the quench strength. We first demonstrate how this can be used to predict the system's temperature after the quench from equilibrium properties at the pre-quench temperature. For a thermalizing post-quench system, it furthermore allows us to calculate equilibrium observable expectation values. Finally, in the presence of additional conserved quantities besides the Hamiltonian, we obtain a hierarchy of necessary conditions for thermalization towards the (post-quench) canonical ensemble. At first order, these thermalization conditions have a nice geometric interpretation in operator space with the canonical covariance as a semi-inner product: The quench operator (difference between post- and pre-quench Hamiltonians) and the conserved quantity must be orthogonal in the orthogonal complement of the post-quench Hamiltonian. We illustrate the results numerically for a variety of setups involving integrable and nonintegrable models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12696 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Temperature and conditions for thermalization after canonical quenches Dabelow, Lennart Statistical Mechanics Quantum Physics We consider quenches of a quantum system that is prepared in a canonical equilibrium state of one Hamiltonian and then evolves unitarily in time under a different Hamiltonian. Technically, our main result is a systematic expansion of the pre- and post-quench canonical ensembles in the quench strength. We first demonstrate how this can be used to predict the system's temperature after the quench from equilibrium properties at the pre-quench temperature. For a thermalizing post-quench system, it furthermore allows us to calculate equilibrium observable expectation values. Finally, in the presence of additional conserved quantities besides the Hamiltonian, we obtain a hierarchy of necessary conditions for thermalization towards the (post-quench) canonical ensemble. At first order, these thermalization conditions have a nice geometric interpretation in operator space with the canonical covariance as a semi-inner product: The quench operator (difference between post- and pre-quench Hamiltonians) and the conserved quantity must be orthogonal in the orthogonal complement of the post-quench Hamiltonian. We illustrate the results numerically for a variety of setups involving integrable and nonintegrable models. |
| title | Temperature and conditions for thermalization after canonical quenches |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2510.12696 |