Chaotic and quantum dynamics in driven-dissipative bosonic chains

TL;DR

This paper studies how a driven-dissipative bosonic chain thermalizes in space, revealing a two-stage process with a prethermal regime and a transition to a nonthermal condensate, using semiclassical chaos indicators and quantum fluctuations.

Contribution

It uncovers the spatial thermalization dynamics and identifies a prethermal regime in driven-dissipative bosonic chains, extending understanding of nonequilibrium steady states.

Findings

Two-stage spatial thermalization with prethermal regime

Emergence of a nonthermal, non-chaotic condensate at strong drives

Extended hydrodynamic regime with anomalous temperature profiles

Abstract

Thermalization in quantum many-body systems typically unfolds over timescales governed by intrinsic relaxation mechanisms. Yet, its spatial aspect is less understood. We investigate this phenomenon in the nonequilibrium steady state (NESS) of a Bose-Hubbard chain subject to coherent driving and dissipation at its boundaries, a setup inspired by current designs in circuit quantum electrodynamics. The dynamical fingerprints of chaos in this NESS are probed using semiclassical out-of-time-order correlators (OTOCs) within the truncated Wigner approximation (TWA). At intermediate drive strengths, we uncover a two-stage thermalization along the spatial dimension: phase coherence is rapidly lost near the drive, while amplitude relaxation occurs over much longer distances. This separation of scales gives rise to an extended hydrodynamic regime exhibiting anomalous temperature profiles, which we designate as a ``prethermal'' domain. At stronger drives, the system enters a nonthermal, non-chaotic finite-momentum condensate characterized by sub-Poissonian photon statistics and a spatially modulated phase profile, whose stability is undermined by quantum fluctuations. We explore the conditions underlying this protracted thermalization in space and argue that similar mechanisms are likely to emerge in a broad class of extended driven-dissipative systems.