Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields

Abstract

We study the BS model, which is a one-dimensional lattice field theory taking real values. Its dynamics is governed by coupled differential equations plus random nearest neighbor exchanges. The BS model has exactly two locally conserved fields. Through numerical simulations the peak structure of the steady state space-time correlations is determined and compared with nonlinear fluctuating hydrodynamics, which predicts a traveling peak with KPZ scaling function and a standing peak with a scaling function given by the completely asymmetric Levy distribution with parameter $\alpha =5/3$. As a by-product, we completely classify the universality classes for two coupled stochastic Burgers equations with arbitrary coupling coefficients.

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• 3/4 Fractional superdiffusion of energy in a system of harmonic oscillators perturbed by a conservative noise
• Universality classes in two-component driven diffusive systems
• Non-KPZ modes in two-species driven diffusive systems

Cited by in corpus (39)

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• Fluctuating hydrodynamics for a discrete Gross-Pitaevskii equation: mapping to Kardar-Parisi-Zhang universality class
• Family-Vicsek Scaling of Roughness Growth in a Strongly Interacting Bose Gas
• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• 3/4 Fractional superdiffusion of energy in a system of harmonic oscillators perturbed by a conservative noise
• Transport in quantum chains under strong monitoring
• Equilibrium dynamical correlations in the Toda chain and other integrable models
• Universality classes in two-component driven diffusive systems
• Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension
• Multi-particle collision simulations of 2D one-component plasmas: anomalous transport and dimensional crossovers
• Tail of the two-time height distribution for KPZ growth in one dimension
• Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions
• Fermi-Pasta-Ulam chains with harmonic and anharmonic long-range interactions
• Equilibration of sinusoidal modulation of temperature in linear and nonlinear chains
• Dynamic scaling relation in quantum many-body systems
• Temperature profile and boundary conditions in an anomalous heat transport model
• Diffusive hydrodynamics from long-range correlations
• The kinetic exclusion process: a tale of two fields
• Thermal conductivity for coupled charged harmonic oscillators with noise in a magnetic field
• Observing Golden Mean Universality Class in the Scaling of Thermal Transport
• Dynamics of coupled modes for sliding particles on a fluctuating landscape
• Perturbative solution for the spectral gap of the weakly asymmetric exclusion process
• Nonlinear Perturbation of a Noisy Hamiltonian Lattice Field Model: Universality Persistence
• Variational approach to renormalized phonon in momentum-nonconserving nonlinear lattices
• A lattice gas model for generic one-dimensional Hamiltonian Systems
• KPZ modes in $d$-dimensional directed polymers
• Hydrodynamic approximations for driven dense colloidal mixtures in narrow pores
• Out-of-time-ordered correlator in the one-dimensional Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations
• Non-linear Fluctuating Hydrodynamics with many conserved fields: the case of a 3D anharmonic chain
• Miscible-Immiscible Transition and Nonequilibrium Scaling in Two-Component Driven Open Condensate Wires
• Super-diffusion and crossover from diffusive to anomalous transport in a one-dimensional system
• Universality in many-body driven systems with an umbilic point
• Quest for the golden ratio universality class
• Kardar-Parisi-Zhang universality in two-component driven diffusive models: Symmetry and renormalization group perspectives
• A Novel Mechanism of Ordering in a Coupled Driven System: Vacancy Induced Phase Separation
• Symmetry-based nonlinear fluctuating hydrodynamics in one dimension
• Universality in driven systems with a multiply-degenerate umbilic point
• Collisional relaxation and dynamical scaling in multiparticle collisions dynamics
• Non-equilibrium stationary properties of the boundary driven zero-range process with long jumps