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

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