Chaos and spatial prethermalization in driven-dissipative bosonic chains

• URL: http://arxiv.org/abs/2409.12225v2
• Date: Mon, 30 Dec 2024 16:06:38 GMT
• Title: Chaos and spatial prethermalization in driven-dissipative bosonic chains
• Authors: Filippo Ferrari, Fabrizio Minganti, Camille Aron, Vincenzo Savona,
• Abstract summary: We investigate the spatial aspect of thermalization in quantum many-body systems. We uncover a two-stage thermalization process along the spatial dimension. We argue that similar prethermal chaotic phases are likely to occur in a broad range of extended driven-dissipative systems.
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• Abstract: Thermalization in quantum many-body systems, the process by which they naturally evolve toward thermal equilibrium, typically unfolds over timescales set by the underlying relaxation mechanisms. Yet, the spatial aspect of thermalization in these systems is less understood. We investigate this phenomenon within the nonequilibrium steady state (NESS) of a Bose-Hubbard chain subject at its boundaries to coherent driving and dissipation, a setup inspired by current designs in circuit quantum electrodynamics. We uncover a two-stage thermalization process along the spatial dimension. Close to the coherent drive, the U(1) symmetry of the phase of the photonic field is restored over a short length scale, while its amplitude relaxes over a much larger scale. This opens up an extensive region of the chain where the photon density remains high, and the chaotic dynamics give rise to a hydrodynamic regime, characterized by local equilibria with a large and slowly-varying effective chemical potential. Dynamical fingerprints of chaos in this NESS are probed using semiclassical out-of-time-order correlators (OTOCs) within the truncated Wigner approximation (TWA). We explore the conditions underlying this protracted thermalization in space and argue that similar prethermal chaotic phases are likely to occur in a broad range of extended driven-dissipative systems.

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