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Thermal Equilibrium of a Macroscopic Quantum System in a Pure State

Author(s): Goldstein, Sheldon; Huse, David A; Lebowitz, Joel L; Tumulka, Roderich

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Abstract: We consider the notion of thermal equilibrium for an individual closed macroscopic quantum system in a pure state, i.e., described by a wave function. The macroscopic properties in thermal equilibrium of such a system, determined by its wave function, must be the same as those obtained from thermodynamics, e.g., spatial uniformity of temperature and chemical potential. When this is true we say that the system is in macroscopic thermal equilibrium (MATE). Such a system may, however, not be in microscopic thermal equilibrium (MITE). The latter requires that the reduced density matrices of small subsystems be close to those obtained from the microcanonical, equivalently the canonical, ensemble for the whole system. The distinction between MITE and MATE is particularly relevant for systems with many-body localization for which the energy eigenfuctions fail to be in MITE while necessarily most of them, but not all, are in MATE. We note, however, that for generic macroscopic systems, including those with MBL, most wave functions in an energy shell are in both MATE and MITE. For a classical macroscopic system, MATE holds for most phase points on the energy surface, but MITE fails to hold for any phase point
Publication Date: Sep-2015
Electronic Publication Date: 4-Sep-2015
Citation: Goldstein, Sheldon, Huse, David A, Lebowitz, Joel L, Tumulka, Roderich. (2015). Thermal Equilibrium of a Macroscopic Quantum System in a Pure State. Physical Review Letters, 115 (10), 10.1103/PhysRevLett.115.100402
DOI: doi:10.1103/PhysRevLett.115.100402
ISSN: 0031-9007
EISSN: 1079-7114
Type of Material: Journal Article
Journal/Proceeding Title: Physical Review Letters
Version: Author's manuscript

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