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

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