Semiclassical Langevin dynamics of long-range dissipative time crystals

• URL: http://arxiv.org/abs/2607.03486v1
• Date: Fri, 03 Jul 2026 16:55:32 GMT
• Title: Semiclassical Langevin dynamics of long-range dissipative time crystals
• Abstract summary: We develop a semiclassical Langevin approach to study finite-size effects in dissipative time-crystalline spin systems.<n>For a spin-$1/2$ model with power-law Lindblad operators, we find finite-size oscillations exponentially decaying in time.<n>We also apply our approach to a spin-one model with local dissipation and long-range Hamiltonian interactions.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a semiclassical Langevin approach to study finite-size effects in dissipative time-crystalline spin systems. For a spin-$1/2$ model with power-law Lindblad operators, we find finite-size oscillations exponentially decaying in time, and their decay rate decreases algebraically with system size in the long-range regime. The scaling exponent of this decay time provides a direct diagnostic of the robustness of the time-crystalline, and we find that this robustness extends beyond the range of power-law dissipation exponents where the system dynamics is mean-field in the thermodynamic limit. We also apply our approach to a spin-one model with local dissipation and long-range Hamiltonian interactions, formulating it in terms of Gell-Mann variables. In this case, finite-size stability is quantified through the deviation time from the mean-field behavior and the behavior of the dominant Fourier peak. We find that both quantities scale as a power law with the system size -- marking thereby a time-crystal behavior -- when the exponent of the power-law interaction is below a certain threshold, that turns out to be in agreement with previous cumulant-expansion findings. Our results show that semiclassical Langevin dynamics provides a useful finite-size probe of dissipative time crystals in regimes beyond exact Lindblad simulations.

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