Time operators and time crystals: self-adjointness by topology change

Nakatsugawa, Keiji; Fujii, T.; Saxena, Avadh; Tanda, Satoshi

doi:10.1088/1751-8121/ab3f46

Title: Time operators and time crystals: self-adjointness by topology change

Journal Article · 18 December 2019 · Journal of Physics. A, Mathematical and Theoretical

DOI: https://doi.org/10.1088/1751-8121/ab3f46 · OSTI ID:1699452

^[1]; Fujii, T. ^[2];

^[3]; Tanda, Satoshi ^[1]

Hokkaido Univ., Sapporo (Japan)
Hokkaido Univ., Sapporo (Japan); Asahikawa Medical Univ. (Japan)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)

We investigate time operators in the context of quantum time crystals in ring systems. A generalized commutation relation called the generalized weak Weyl relation is used to derive a class of self-adjoint time operators for ring systems with a periodic time evolution: The conventional Aharonov–Bohm time operator is obtained by taking the infinite-radius limit. Then, we discuss the connection between time operators, time crystals and real-space topology. We also reveal the relationship between our time operators and a $ΡΤ$-symmetric time operator. These time operators are then used to derive several energy-time uncertainty relations.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1699452

Report Number(s):: LA-UR--17-30802

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 2 Vol. 53; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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