Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1502.06661

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

Manas Kulkarni·David A. Huse·Herbert Spohn
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cond-mat.quant-gascond-mat.stat-mechmath-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Manas Kulkarni, David A. Huse, Herbert Spohn. 2015-02-24. Fluctuating hydrodynamics for a discrete Gross-Pitaevskii equation: mapping to Kardar-Parisi-Zhang universality class. https://doi.org/10.1103/physreva.92.043612

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Ab initio path-integral Monte Carlo results for the one-particle spectral function of the warm dense electron gas

We present quasi-exact \emph{ab initio} path-integral Monte Carlo results for the Matsubara Green's function of the uniform electron gas (UEG) at finite temperature over a broad range of coupling strengths ($r_s=1,\dots,10)$. We further extract the static self-energy $Σ_\infty(p)$ and perform an analytic continuation for spectral function $A(p,ω)$, conclusively ruling out the possibility of distinct satellite features at these conditions. In addition, our work opens up intriguing avenues to study the single-particle spectrum and density of states of real warm dense matter systems based on first principles.

cond-mat.quant-gas↗
arXiv2026

Non-Hermitian engineering of superfluidity in a Rashba spin-orbit-coupled Fermi gas

We investigate superfluid pairing in a two-dimensional Rashba spin-orbit-coupled Fermi gas subject to spin-selective one-body loss. Within the non-Hermitian mean-field framework, we self- consistently solve the gap and number equations and find that moderate dissipation can significantly enhance the pairing gap, resulting in a pronounced nonmonotonic dependence on the dissipation strength. Dissipation also provides an additional control parameter for driving the system across the BCS-BEC crossover. We further analyze the quasi-particle spectrum and identify two distinct superfluid regimes characterized by one and three exceptional rings, separated by an exceptional spectral transition. Interestingly, dissipation can enhance both pairing channels while simultaneously inducing a momentum-dependent phase twist in the triplet component. These results demonstrate that spin-selective dissipation provides a versatile non-Hermitian control knob for manipulating superfluid pairing, spectral structure, and crossover physics in spin-orbit-coupled quantum gases.

cond-mat.quant-gas↗
arXiv2026

Quantum dynamics of spinful impurity in ideal Bose gas

We discuss the quench dynamics of an isolated system composed of a single spinful impurity in the transverse Rabi field and bath of non-interacting three- and two-dimensional bosons. Specifically, we consider the evolution of bosons and a spin-$\frac{1}{2}$ particle, initially prepared in a Bose-Einstein condensate state and a magnetic ground state, respectively, with the spin-dependent contact boson-impurity interaction switched on. Applying an original mean-field-like approximation, which naturally reflects the statistical effects of the bosonic bath, we calculate time-dependent components of the average impurity spin and the overlap of the wave function between initial and arbitrary time moments. A key prediction is a substantial speed-up in the decoherence (thermalization) dynamics of the spin degree of freedom compared to results obtained with the Chevy-like ansatz.

cond-mat.quant-gas↗