Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems

TL;DR

This paper investigates how non-Markovian environments influence relaxation dynamics in quantum many-body systems, revealing a complex phase diagram with different relaxation regimes including exponential and algebraic decay.

Contribution

It introduces a detailed analysis of an open SYK model coupled to a pseudogapped bath, uncovering new relaxation behaviors driven by non-Markovian dissipation.

Findings

Identification of bath-driven power-law relaxation regimes

Discovery of chaos-driven exponential decay in the system

Observation of an intermediate pre-relaxation phase with crossover behavior

Abstract

In interacting quantum many-body systems, relaxation toward equilibrium reflects a competition between internal chaotic dynamics and environmental dissipation. While conventional Markovian baths typically produce exponential decay, non-Markovian dissipation can give rise to more intricate behavior, including algebraic relaxation. We study an open Sachdev-Ye-Kitaev (SYK) model coupled to a pseudogapped fermionic bath, using the Keldysh formalism to compute steady-state correlations in the large-$N$ limit. Our results uncover a rich dynamical phase diagram, with regimes of bath-driven power-law relaxation, chaos-driven exponential decay, and an intermediate pre-relaxation phase where exponential decay crosses over to algebraic decay. These findings demonstrate that non-Markovian environments can qualitatively reshape relaxation mechanisms in strongly correlated quantum many-body systems.