Topological and nonlinearity-induced thermalization in a PT-symmetric split-Langevin bath

TL;DR

This paper explores how PT-symmetry and nonlinearity influence thermalization and steady states in classical chains with gain and loss, revealing topological effects and stabilization mechanisms.

Contribution

It introduces the concept of a split Langevin bath in PT-symmetric systems, analyzing topological and nonlinear effects on thermalization and steady states.

Findings

Split Langevin bath can prevent thermalization or create inhomogeneous temperature profiles.

Topological phase of the chain affects steady-state properties.

Nonlinearity stabilizes modes, leading to thermalization regardless of gain-loss placement.

Abstract

Open classical systems with balanced, separated gain and loss, called PT-symmetric systems, have been extensively studied over the past decade. Here, we investigate the properties of a uniform, harmonic chain with spatially separated viscous loss and stochastic gain that are only statistically balanced. We show that such a "split Langevin" bath leads to either the absence of thermalization or non-equilibrium steady states with inhomogeneous temperature profile, both of which are understood in terms of normal modes of the chain. With a Su-Schrieffer-Heeger (SSH) chain, a canonical model with topological edge modes, we show that the steady-state properties reflect the topological phase of the underlying chain. We also show that nonlinearity stabilizes the amplifying modes in a harmonic chain, thereby leading to thermalization irrespective of the gain and loss locations. Our results expand the pool of possible realizations of non-Hermitian models to the stochastic domain.