Nonlinear fluctuating hydrodynamics for anharmonic chains. (English) Zbl 1291.82119

Summary: With focus on anharmonic chains, we develop a nonlinear version of fluctuating hydrodynamics, in which the Euler currents are kept to second order in the deviations from equilibrium and dissipation plus noise are added. The required model-dependent parameters are written in such a way that they can be computed numerically within seconds, once the interaction potential, pressure, and temperature are given. In principle the theory is applicable to any one-dimensional system with local conservation laws. The resulting nonlinear stochastic field theory is handled in the one-loop approximation. Some of the large scale predictions can still be worked out analytically. For more details one has to rely on numerical simulations of the corresponding mode-coupling equations. In this way we arrive at detailed predictions for the equilibrium time correlations of the locally conserved fields of an anharmonic chain.


82D15 Statistical mechanics of liquids
35Q31 Euler equations
35Q53 KdV equations (Korteweg-de Vries equations)
82-08 Computational methods (statistical mechanics) (MSC2010)
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
Full Text: DOI arXiv


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