Time operators and time crystals: self-adjointness by topology change. (19th December 2019)

• Record Type: Journal Article
• Authors: Nakatsugawa, K; Fujii, T; Saxena, A; Tanda, S
• Is Part Of: Journal of physics. Volume 53:Number 2(2020)
• Publication Date: 2019-12-19
• Subjects: time operator -- topology -- uncertainty relations -- PT-symmetry -- time crystal; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab3f46
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: 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 -symmetric time operator. These time operators are then used to derive several energy-time uncertainty relations.