### 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 a 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 nonzero temperature dynamical structure factor and its scaling form and exponent. Given the ubiquity of the Gross-Pitaevskii equation (also known as the nonlinear Schrödinger 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.

Original language | English (US) |
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Article number | 043612 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 92 |

Issue number | 4 |

DOIs | |

State | Published - Oct 16 2015 |

### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics