Absence of Quantum Time Crystals
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In analogy with crystalline solids around us, Wilczek recently proposed the idea of "time crystals" as phases that spontaneously break the continuous time translation into a discrete subgroup. The proposal stimulated further studies and vigorous debates whether it can be realized in a physical system. However, a precise definition of the time crystal is needed to resolve the issue. Here we first present a definition of time crystals based on the time-dependent correlation functions of the order parameter. We then prove a no-go theorem that rules out the possibility of time crystals defined as such, in the ground state or in the canonical ensemble of a general Hamiltonian, which consists of not-too-long-range interactions.
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Cited by 4 Pith papers
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Spin-induced noncommutativity in the Bateman oscillator yields discrete scaling covariance in amplified and damped modes, producing self-similar evolution and history-dependent non-Markovian reduced dynamics.
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Spin-Induced Non-Markovian Time-Crystal-Like Dynamics and Fractal Scaling in the Bateman Dual Oscillator
Spin-induced deformation in the Bateman dual oscillator framework yields non-Markovian reduced dynamics with persistent oscillations and fractal scaling that mimic time crystals in a globally unitary quantum system.
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Spin-Induced Non-Markovian Time-Crystal-Like Dynamics and Fractal Scaling in the Bateman Dual Oscillator
Spin-induced deformation creates a Bateman dual oscillator whose reduced non-Markovian dynamics produces time-crystal-like ordering and fractal scaling in a closed quantum system.
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On prethermal time crystals from semi-holography
Semi-holographic systems with perturbative and holographic sectors exhibit prethermal time crystals through dissipationless modes in hydrodynamic channels plus short-wavelength instabilities that produce inhomogeneiti...
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