Christian B. Mendl, Herbert Spohn
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. The only input parameters required are the average equilibrium currents and the static susceptibilities of the conserved fields. In our context 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 equation has a quadratic memory kernel and describes the time evolving correlator matrix of all locally conserved fields. Long time asymptotics is computed analytically and finite time properties are obtained through a numerical simulation of the mode-coupling equations, which provide predictions still to be compared with data from molecular dynamics.
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http://arxiv.org/abs/1305.1209
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