Macroscopic Irreversibility in Quantum Systems: Free Expansion in a Fermion Chain

[2401.15263] Macroscopic Irreversibility in Quantum Systems: Free Expansion in a Fermion Chain Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Statistical Mechanics arXiv:2401.15263 (cond-mat) [Submitted on 27 Jan 2024 ( v1 ), last revised 25 May 2025 (this version, v4)] Title: Macroscopic Irreversibility in Quantum Systems: Free Expansion in a Fermion Chain Authors: Hal Tasaki View a PDF of the paper titled Macroscopic Irreversibility in Quantum Systems: Free Expansion in a Fermion Chain, by Hal Tasaki View PDF HTML (experimental) Abstract: We consider a free fermion chain with uniform nearest-neighbor hopping and let it evolve from an arbitrary initial state with a fixed macroscopic number of particles. We then prove that, at a sufficiently large and typical time, the measured coarse-grained density distribution is almost uniform with (quantum mechanical) probability extremely close to one. This establishes the emergence of irreversible behavior, i.e., a ballistic diffusion, in a system governed by quantum mechanical unitary time evolution. It is conceptually important that irreversibility from any initial state is proved here without introducing any randomness to the initial state or the Hamiltonian, while the known examples, both classical and quantum, rely on certain randomness or apply to limited classes of initial states. The essential new ingredient in the proof is the large deviation bound for every energy eigenstate, which is reminiscent of the strong ETH (energy eigenstate thermalization hypothesis). Comments: 5 pages, no figures. This is the final version to be published in PRE as a Letter. There are also some new references. There is a 20-minute video that explains the main results of the present work: this https URL Subjects: Statistical Mechanics (cond-mat.stat-mech) ; Mathematical Physics (math-ph); Quantum Physics (quant-ph) Cite as: arXiv:2401.15263 [cond-mat.stat-mech] (or arXiv:2401.15263v4 [cond-mat.stat-mech] for this version) https://doi.org/10.48550/arXiv.2401.15263 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. E 111, L062103 (2025) Related DOI : https://doi.org/10.1103/8cdf-sth8 Focus to learn more DOI(s) linking to related resources Submission history From: Hal Tasaki [ view email ] [v1] Sat, 27 Jan 2024 01:34:09 UTC (10 KB) [v2] Fri, 2 Feb 2024 14:14:12 UTC (11 KB) [v3] Fri, 10 May 2024 02:41:12 UTC (12 KB) [v4] Sun, 25 May 2025 13:07:39 UTC (12 KB) Full-text links: Access Paper: View a PDF of the paper titled Macroscopic Irreversibility in Quantum Systems: Free Expansion in a Fermion Chain, by Hal Tasaki View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.stat-mech < prev | next > new | recent | 2024-01 Change to browse by: cond-mat math math-ph math.MP quant-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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