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

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.

6 pages, 2 figures

References in corpus (7)

• Heat Transport in low-dimensional systems
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Exact scaling functions for one-dimensional stationary KPZ growth
• Rigorous Derivation of the Gross-Pitaevskii Equation
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
• Low temperature dynamics of the one-dimensional discrete nonlinear Schrödinger equation

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