Phases of Quench Dynamics in the Presence of Fluctuation

TL;DR

This paper investigates how thermal fluctuations influence quench dynamics in a system with $Z_2$ symmetry, revealing a phase diagram with three distinct dynamical regimes and modified scaling behaviors.

Contribution

It introduces a phase diagram for quench dynamics considering thermal fluctuations, highlighting three phases and their characteristics near the critical point.

Findings

Identified three phases with distinct relaxation behaviors.

Modified Kibble-Zurek scaling in small fluctuation, slow quench regime.

Enhanced fluctuations significantly affect the phase boundaries.

Abstract

We study the effect of thermal fluctuations on a sourced quench in a system with $Z_2$ symmetry. By ignoring the fluctuation of finite momentum modes and tracing the dynamics of zero momentum mode driven by a spatially homogeneous source near the critical point, we map out a phase diagram for the quench dynamics. The phase diagram consists of three different phases. Phase I occurs for large fluctuations with the relaxation time set by fluctuation induced inverse effective mass square. Phase II occurs for small fluctuation and slow quench rate. The dynamics is characterized by a modified Kibble-Zurek scaling. Phase III corresponds to small fluctuations and rapid quench rate. The relaxation time tends to a finite value in the rapid quench limit. We also estimate the fluctuations of finite momentum modes, finding significant enhancement of the effective mass square. We speculate the qualitative features of the phase diagram may remain the same, but enhanced fluctuations can lead to shrinkage of phase II and III.