We show that time translation symmetry of a ring system with a macroscopic quantum ground state is broken by decoherence. In particular, we consider a ring-shaped incommensurate charge density wave (ICDW ring) threaded by a fluctuating magnetic flux: the Caldeira-Leggett model is used to model the fluctuating flux as a bath of harmonic oscillators. We show that the charge density expectation value of a quantized ICDW ring coupled to its environment oscillates periodically. The Hamiltonians considered in this model are time independent unlike ``Floquet time crystals'' considered recently. Our model forms a metastable quantum time crystal with a finite length in space and in time.We show that time translation symmetry of a ring system with a macroscopic quantum ground state is broken by decoherence. In particular, we consider a ring-shaped incommensurate charge density wave (ICDW ring) threaded by a fluctuating magnetic flux: the Caldeira-Leggett model is used to model the fluctuating flux as a bath of harmonic oscillators. We show that the charge density expectation value of a quantized ICDW ring coupled to its environment oscillates periodically. The Hamiltonians considered in this model are time independent unlike ``Floquet time crystals'' considered recently. Our model forms a metastable quantum time crystal with a finite length in space and in time.

arXiv:1703.04002Physical review. B./Physical review. BSep 20, 201723 citations

QUANTUM DECOHERENCE AND TIME SYMMETRY BREAKING

Tomio Yamakoshi Petrosky, Valeri Abulevich Barsegov

Advanced series in astrophysics and cosmologyMay 1, 20000 citations

Incommensurate Charge Density Wave as Quantum Space-Time Crystal

Keiji Nakatsugawa, Toshiyuki Fujii, Satoshi Tanda

A quantum time crystal (QTC) is a novel quantum mechanical ground state that was recently proposed by Wilczek. Although many QTC models have been proposed, it is not clear yet if such states are possible. We propose the idea that an incommensurate charge density wave (ICDW) forms a quantum space crystal (QSC), which is an extension of a QTC in the spatial domain. Consequently, a rotating ring-shaped ICDW naturally forms a quantum space-time crystal (QSTC), which combines the two concepts of QTC and QSC. The breaking of space-time translation symmetry is understood using time-dependent density matrices. Furthermore, we show that this model can be observed in real systems such as TaS $_3$ ring crystals at finite temperature. Our results suggest that QTC/QSTC can exist.A quantum time crystal (QTC) is a novel quantum mechanical ground state that was recently proposed by Wilczek. Although many QTC models have been proposed, it is not clear yet if such states are possible. We propose the idea that an incommensurate charge density wave (ICDW) forms a quantum space crystal (QSC), which is an extension of a QTC in the spatial domain. Consequently, a rotating ring-shaped ICDW naturally forms a quantum space-time crystal (QSTC), which combines the two concepts of QTC and QSC. The breaking of space-time translation symmetry is understood using time-dependent density matrices. Furthermore, we show that this model can be observed in real systems such as TaS$_3$ ring crystals at finite temperature. Our results suggest that QTC/QSTC can exist.

arXiv:1510.01830Oct 7, 20150 citations

Time-Periodic Quantum Systems

L. E. Reichl

Fundamental theories of physicsJan 1, 20212 citations

Time Operators and Time Crystals

Keiji Nakatsugawa, Toshiyuki Fujii, Avadh Saxena +1 more

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 $\mathcal{PT}$ -symmetric time operator. These time operators are then used to derive several energy-time uncertainty relations.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 $\mathcal{PT}$-symmetric time operator. These time operators are then used to derive several energy-time uncertainty relations.

arXiv:1711.10179Nov 28, 20170 citations

_3

ring crystals at finite temperature. Our results suggest that QTC/QSTC can exist.

\mathcal{PT}

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