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arXiv · 1311.4386

Lattice Monte Carlo methods for systems far from equilibrium

David Mesterházy·Luca Biferale·Karl Jansen·Raffaele Tripiccione
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Abstract

We present a new numerical Monte Carlo approach to determine the scaling behavior of lattice field theories far from equilibrium. The presented methods are generally applicable to systems where classical-statistical fluctuations dominate the dynamics. As an example, these methods are applied to the random-force-driven one-dimensional Burgers' equation - a model for hydrodynamic turbulence. For a self-similar forcing acting on all scales the system is driven to a nonequilibrium steady state characterized by a Kolmogorov energy spectrum. We extract correlation functions of single- and multi-point quantities and determine their scaling spectrum displaying anomalous scaling for high-order moments. Varying the external forcing we are able to tune the system continuously from equilibrium, where the fluctuations are short-range correlated, to the case where the system is strongly driven in the infrared. In the latter case the nonequilibrium scaling of small-scale fluctuations are shown to be universal.

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David Mesterházy, Luca Biferale, Karl Jansen, Raffaele Tripiccione. 2013-11-18. Lattice Monte Carlo methods for systems far from equilibrium. https://arxiv.org/abs/1311.4386

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