Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics

Abstract

We study the equilibrium time correlations for the conserved fields of classical anharmonic chains and argue that their dynamic correlator can be predicted on the basis of nonlinear fluctuating hydrodynamics. In fact our scheme is more general and would cover also other one-dimensional hamiltonian systems, for example classical and quantum fluids. Fluctuating hydrodynamics is a nonlinear system of conservation laws with noise. For a single mode it is equivalent to the noisy Burgers equation, for which explicit solutions are available. Our focus is the case of several modes. No exact solutions have been found so far and we rely on a one-loop approximation. The resulting mode-coupling equations have a quadratic memory kernel and describe the time evolving 3 x 3 correlator matrix of the locally conserved fields. Long time asymptotics is computed analytically and finite time properties are obtained through a numerical simulation of the mode-coupling equations.

2 figures

References in corpus (5)

• Exact scaling functions for one-dimensional stationary KPZ growth
• Energy diffusion in hard-point systems
• Coupled Kardar-Parisi-Zhang Equations in One Dimension
• Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains
• Collective mode damping and viscosity in a 1D unitary Fermi gas

Cited by in corpus (89)

• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Fibonacci family of dynamical universality classes
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Diffusive hydrodynamics from integrability breaking
• Kardar-Parisi-Zhang Scaling for an Integrable Lattice Landau-Lifshitz Spin Chain
• Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
• Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion
• Current fluctuations for anharmonic chains in thermal equilibrium
• Equilibrium time-correlation functions for one-dimensional hard-point systems
• Non-Fourier heat transport in nanosystems
• Fluctuating hydrodynamics for a discrete Gross-Pitaevskii equation: mapping to Kardar-Parisi-Zhang universality class
• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Classical many-body chaos with and without quasiparticles
• Generalized hydrodynamics: a perspective
• Integrable Matrix Models in Discrete Space-Time
• A violation of universality in anomalous Fourier's law
• Equilibrium dynamical correlations in the Toda chain and other integrable models
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain
• Nonequilibrium Steady State in Open Quantum Systems: Influence Action, Stochastic Equation and Power Balance
• Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process
• Low temperature dynamics of the one-dimensional discrete nonlinear Schrödinger equation
• Universality classes in two-component driven diffusive systems
• Wave Turbulence and thermalization in one-dimensional chains
• Heat transport via low-dimensional systems with broken time-reversal symmetry
• Non-KPZ modes in two-species driven diffusive systems
• Transport in perturbed classical integrable systems: the pinned Toda chain
• Diffusion from Convection
• Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension
• Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
• The Fourier heat conduction as a strong kinetic effect
• Fractional diffusion equation description of an open anomalous heat conduction set-up
• Coupled transport in rotor models
• The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas
• Renormalized phonons in nonlinear lattices: A variational approach
• Fourier's law based on microscopic dynamics
• Crossover between different universality classes: Scaling for thermal transport in one dimension
• Nonequilibrium phonon mean free paths in anharmonic chains
• Transport properties of the classical Toda chain: effect of a pinning potential
• Non-universality of front fluctuations for compact colonies of non-motile bacteria
• Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation
• Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map
• Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions
• Diffusive hydrodynamics from long-range correlations
• Dynamic criticality far-from-equilibrium: one-loop flow of Burgers-Kardar-Parisi-Zhang systems with broken Galilean invariance
• Pressure-induced recovery of Fourier's law in one dimensional momentum-conserving systems
• Marching on a rugged landscape: Universality in disordered asymmetric exclusion processes
• Nonequilibrium criticality driven by Kardar-Parisi-Zhang fluctuations in the synchronization of oscillator lattices
• Underlying mechanisms for normal heat transport in one-dimensional anharmonic oscillator systems with a double-well interparticle interaction
• Kardar-Parisi-Zhang universality class for the critical dynamics of reaction-diffusion fronts
• The kinetic exclusion process: a tale of two fields
• One-Dimensional Self-Organization and Nonequilibrium Phase Transition in a Hamiltonian System
• Shocks, rarefaction waves, and current fluctuations for anharmonic chains
• Dynamics of fluctuation correlation in periodically driven classical system
• Observing Golden Mean Universality Class in the Scaling of Thermal Transport
• Heat conduction and energy diffusion in momentum-conserving 1D full lattice ding-a-ling model
• Ordered phases in coupled nonequilibrium systems: dynamic properties
• The derivative of the Kardar-Parisi-Zhang equation is not in the KPZ universality class
• Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential
• Light and heavy particles on a fluctuating surface: Bunchwise balance, irreducible sequences and local density-height correlations
• Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices
• Gaussian statistics as an emergent symmetry of the stochastic Burgers equation
• Stretch diffusion and heat conduction in 1D nonlinear lattices
• Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction
• Hydrodynamics and transport in the long-range-interacting ${\phi }^4$ chain
• Thermal transport of confined water molecules in quasi-one-dimensional nanotubes
• Nonequilibrium Steady State and Heat Transport in Nonlinear Open Quantum Systems: Stochastic Influence Action and Functional Perturbative Analysis
• Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport
• Heat perturbations spreading in the Fermi-Pasta-Ulam-$\beta$ system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity
• KPZ modes in $d$-dimensional directed polymers
• Large-scale fluctuations of the largest Lyapunov exponent in diffusive systems
• Temperature dependent divergence of thermal conductivity in momentum conserving 1D lattice with asymmetric potential
• First-principle validation of Fourier's law in d=1,2,3 classical systems
• Super diffusive length dependent thermal conductivity in one-dimensional materials with structural defects: longitudinal to transverse phonon scattering leads to $\kappa \propto L^{1/3}$ law
• Infinite family of universal profiles for heat current statistics in Fourier's law
• Scaling of energy spreading in a disordered Ding-Dong lattice
• Autonomous Circular Heat Engine
• Universal spatio-temporal scaling of distortions in a drifting lattice
• Energy current cumulants in one-dimensional systems in equilibrium
• Effect of relative timescale on a system of particles sliding on a fluctuating energy landscape: Exact derivation of product measure condition
• Random initial data and average shock time in the Fermi-Pasta-Ulam-Tsingou chain
• Collisional relaxation and dynamical scaling in multiparticle collisions dynamics
• A Novel Mechanism of Ordering in a Coupled Driven System: Vacancy Induced Phase Separation
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport
• Symmetry-based nonlinear fluctuating hydrodynamics in one dimension
• Entropy production for quasi-adiabatic parameter changes dominated by hydrodynamics