Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain

Abstract

Recent work has developed a nonlinear hydrodynamic fluctuation theory for a chain of coupled anharmonic oscillators governing the conserved fields, namely stretch, momentum, and energy. The linear theory yields two propagating sound modes and one diffusing heat mode. In contrast, the nonlinear theory predicts that, at long times, the sound mode correlations satisfy Kardar-Parisi-Zhang (KPZ) scaling, while the heat mode correlations satisfies Levy-walk scaling. In the present contribution we report on molecular dynamics simulations of Fermi-Pasta-Ulam chains to compute various spatiotemporal correlation functions and compare them with the predictions of the theory. We find very good agreement in many cases, but also some deviations.

11 pages, 10 figures

References in corpus (7)

• Heat Transport in low-dimensional systems
• Exact scaling functions for one-dimensional stationary KPZ growth
• A momentum conserving model with anomalous thermal conductivity in low dimension
• Local Temperature and Universal Heat Conduction in FPU chains
• Self-Consistent Mode-Coupling Approach to 1D Heat Transport
• Anomalous energy transport in the FPU-beta chain
• Crossover from Fermi-Pasta-Ulam to normal diffusive behaviour in heat conduction through open anharmonic lattices

Cited by in corpus (17)

• Lévy walks
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
• Infinite densities for Lévy walks
• Current fluctuations for anharmonic chains in thermal equilibrium
• 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
• Crossover from ballistic to normal heat transport in the ${\varphi }^4$ lattice: If nonconservation of momentum is the reason, what is the mechanism?
• Equilibrium dynamical correlations in the Toda chain and other integrable models
• Phonon hydrodynamics in crystalline materials
• 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
• Renormalized phonons in nonlinear lattices: A variational approach
• Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map
• Nonequilibrium Steady State and Heat Transport in Nonlinear Open Quantum Systems: Stochastic Influence Action and Functional Perturbative Analysis
• Large-scale fluctuations of the largest Lyapunov exponent in diffusive systems
• Thermal conductance of suspended nanoribbons: interplay between strain and interatomic potential nonlinearity