Fluctuating hydrodynamics for a discrete Gross-Pitaevskii equation: mapping to Kardar-Parisi-Zhang universality class

TL;DR

This paper demonstrates that the low-temperature hydrodynamics of a discrete Gross-Pitaevskii equation can be mapped to the Kardar-Parisi-Zhang universality class, providing new insights into its chaotic dynamics and scaling behavior.

Contribution

It introduces a novel mapping of the discrete GPE to a nonlinear fluctuating hydrodynamics framework, specifically to the KPZ equation, validated through numerical benchmarks.

Findings

Mapping to KPZ accurately describes the dynamical structure factor.

Scaling exponents match those predicted by KPZ universality.

The approach applies broadly to systems described by the GPE.

Abstract

We show that several aspects of the low-temperature hydrodynamics of a discrete Gross-Pitaevskii equation (GPE) can be understood by mapping it to a nonlinear version of fluctuating hydrodynamics. This is achieved by first writing the GPE in a hydrodynamic form of a continuity and an Euler equation. Respecting conservation laws, dissipation and noise due to the system's chaos are added, thus giving us a nonlinear stochastic field theory in general and the Kardar-Parisi-Zhang (KPZ) equation in our particular case. This mapping to KPZ is benchmarked against exact Hamiltonian numerics on discrete GPE by investigating the non-zero temperature dynamical structure factor and its scaling form and exponent. Given the ubiquity of the Gross-Pitaevskii equation (a.k.a. nonlinear Schrodinger equation), ranging from nonlinear optics to cold gases, we expect this remarkable mapping to the KPZ equation to be of paramount importance and far reaching consequences.