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Mathematical Physics

arXiv:2201.06051 (math-ph)
[Submitted on 16 Jan 2022 (v1), last revised 30 Aug 2023 (this version, v2)]

Title:Nonexistence of spontaneous symmetry breakdown of time-translation symmetry on general quantum systems: Any macroscopic order parameter moves not!

Authors:Hajime Moriya
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Abstract:This review informs that the impossibility of genuine quantum time crystals has been known in the C*-algebraic quantum statistical mechanics since 1970s. The KMS condition implies that spontaneous breakdown of time-translation symmetry is impossible in general quantum systems. In particular, any non-trivial order, such as periodic, quasi-periodic, and chaotic order cannot exist in the time direction of equilibrium states, meaning that genuine quantum time crystals are excluded from the outset.
Comments: This is a review paper to be published in Reviews in Mathematical Physics
Subjects: Mathematical Physics (math-ph)
MSC classes: 82B03, 82B10
Cite as: arXiv:2201.06051 [math-ph]
  (or arXiv:2201.06051v2 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.2201.06051
Journal reference: Reviews in Mathematical Physics Vol. 36, No. 02, 2330008 (2024) Review Paper
Related DOI: https://doi.org/10.1142/S0129055X2330008X

Submission history

From: Hajime Moriya [view email]
[v1] Sun, 16 Jan 2022 14:04:14 UTC (27 KB)
[v2] Wed, 30 Aug 2023 09:38:37 UTC (27 KB)
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