Quantum Time Crystal By Decoherence: Proposal With Incommensurate Charge Density Wave Ring

Abstract

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.

17 pages, 4 figures

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• Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries
• A dissipative time crystal with or without ${\mathbb{Z}}_2$ symmetry breaking
• Lack of a genuine time crystal in a chiral soliton model
• Quantum dynamics of Dissipative Kerr solitons
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• Nonexistence of spontaneous symmetry breakdown of time-translation symmetry on general quantum systems: Any macroscopic order parameter moves not!
• Critical behavior of a programmable time-crystal lattice gas
• The Nakano-Nishijima-Gell-Mann Formula From Discrete Galois Fields