Timescale for macroscopic equilibration in isolated quantum systems: a rigorous derivation for free fermions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908835341402112 |
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| author | Hara, Takashi Koike, Tatsuhiko |
| author_facet | Hara, Takashi Koike, Tatsuhiko |
| contents | For a class of translation-invariant free-fermion systems (including those with uniform nearest neighbor hopping) on a $d$-dimensional $L \times \cdots \times L$ hypercubic lattice, we prove that, starting from an arbitrary pure initial state, the system equilibrates with respect to the coarse-grained density within a timescale of order $L$. This scaling is optimal, since there exist initial states whose equilibration requires time of order $L$. Our result establishes $O(L)$ as the equilibration timescale, as is expected in normal macroscopic systems with a conserved quantity, such as total number of particles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14096 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Timescale for macroscopic equilibration in isolated quantum systems: a rigorous derivation for free fermions Hara, Takashi Koike, Tatsuhiko Mathematical Physics Statistical Mechanics 82C10, 82C03 For a class of translation-invariant free-fermion systems (including those with uniform nearest neighbor hopping) on a $d$-dimensional $L \times \cdots \times L$ hypercubic lattice, we prove that, starting from an arbitrary pure initial state, the system equilibrates with respect to the coarse-grained density within a timescale of order $L$. This scaling is optimal, since there exist initial states whose equilibration requires time of order $L$. Our result establishes $O(L)$ as the equilibration timescale, as is expected in normal macroscopic systems with a conserved quantity, such as total number of particles. |
| title | Timescale for macroscopic equilibration in isolated quantum systems: a rigorous derivation for free fermions |
| topic | Mathematical Physics Statistical Mechanics 82C10, 82C03 |
| url | https://arxiv.org/abs/2602.14096 |