Dynamical regimes of finite temperature discrete nonlinear Schr\"odinger chain

TL;DR

This paper identifies three distinct dynamical regimes in the finite temperature discrete nonlinear Schrödinger chain using thermodynamic, conserved quantity, and chaos indicators, advancing understanding of its complex behavior.

Contribution

It demonstrates the existence of three temperature-dependent dynamical regimes in DNLS and introduces multiple methods to identify these regimes, including thermodynamics and chaos analysis.

Findings

Three regimes: ultra-low, low, and high temperature.

Crossover temperatures are consistent across methods.

Different approaches can identify dynamical regimes in many-body systems.

Abstract

We show that the one dimensional discrete nonlinear Schr\"odinger chain (DNLS) at finite temperature has three different dynamical regimes (ultra-low, low and high temperature regimes). This has been established via (i) one point macroscopic thermodynamic observables (temperature $T$ , energy density $\epsilon$ and the relationship between them), (ii) emergence and disappearance of an additional almost conserved quantity (total phase difference) and (iii) classical out-of-time-ordered correlators (OTOC) and related quantities (butterfly speed and Lyapunov exponents). The crossover temperatures $T_{\textit{l-ul}}$ (between low and ultra-low temperature regimes) and $T_{\textit{h-l}}$ (between high and low temperature regimes) extracted from these three different approaches are consistent with each other. The analysis presented here is an important step forward towards the understanding of DNLS which is ubiquitous in many fields and has a non-separable Hamiltonian form. Our work also shows that the different methods used here can serve as important tools to identify dynamical regimes in other interacting many body systems.