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

Spohn, Herbert

J. Stat. Phys. 154, No. 5, 1191-1227 (2014).

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.

MSC:

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

Keywords:

classical anharmonic chains; equilibrium time correlations; KPZ scaling; levy stable law

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