Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system

[2310.18880] Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Statistical Mechanics arXiv:2310.18880 (cond-mat) [Submitted on 29 Oct 2023 ( v1 ), last revised 19 Feb 2024 (this version, v2)] Title: Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system Authors: Naoto Shiraishi , Hal Tasaki View a PDF of the paper titled Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system, by Naoto Shiraishi and Hal Tasaki View PDF HTML (experimental) Abstract: We show, without relying on any unproven assumptions, that a low-density free fermion chain exhibits thermalization in the following (restricted) sense. We choose the initial state as a pure state drawn randomly from the Hilbert space in which all particles are in half of the chain. This represents a nonequilibrium state such that the half chain containing all particles is in equilibrium at infinite temperature, and the other half chain is a vacuum. We let the system evolve according to the unitary time evolution determined by the Hamiltonian and, at a sufficiently large typical time, measure the particle number in an arbitrary macroscopic region in the chain. In this setup, it is proved that the measured number is close to the equilibrium value with probability very close to one. Our result establishes the presence of thermalization in a concrete model in a mathematically rigorous manner. The most important theoretical ingredient for the proof of thermalization is the demonstration that a nonequilibrium initial state generated as above typically has a sufficiently large effective dimension. Here, we first give general proof of thermalization based on two assumptions, namely, the absence of degeneracy in energy eigenvalues and a property about the particle distribution in energy eigenstates. We then justify these assumptions in a concrete free-fermion model, where the absence of degeneracy is established by using number-theoretic results. This means that our general result also applies to any lattice gas models in which the above two assumptions are justified. To confirm the potential wide applicability of our theory, we discuss some other models for which the essential assumption about the particle distribution is easily verified, and some non-random initial states whose effective dimensions are sufficiently large. Comments: 33 pages, 0 figures. In version 2, Appendix D on finite temperature extension has been added, and upper bounds for N in Theorems 3.1 and 3.2 have been removed. Some important references have been added. There is a 27-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:2310.18880 [cond-mat.stat-mech] (or arXiv:2310.18880v2 [cond-mat.stat-mech] for this version) https://doi.org/10.48550/arXiv.2310.18880 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J Stat Phys 191, 82 (2024) Related DOI : https://doi.org/10.1007/s10955-024-03289-6 Focus to learn more DOI(s) linking to related resources Submission history From: Hal Tasaki [ view email ] [v1] Sun, 29 Oct 2023 02:48:11 UTC (33 KB) [v2] Mon, 19 Feb 2024 12:59:45 UTC (35 KB) Full-text links: Access Paper: View a PDF of the paper titled Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system, by Naoto Shiraishi and Hal Tasaki View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.stat-mech < prev | next > new | recent | 2023-10 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... 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