Lattice Monte Carlo methods for systems far from equilibrium
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 classicalstatistical fluctuations dominate the dynamics. As an example, these methods are applied to the randomforcedriven onedimensional Burgers' equation  a model for hydrodynamic turbulence. For a selfsimilar 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 multipoint quantities and determine their scaling spectrum displaying anomalous scaling for highorder moments. Varying the external forcing we are able to tune the system continuously from equilibrium, where the fluctuations are shortrange correlated, to the case where the system is strongly driven in the infrared. In the latter case the nonequilibrium scaling of smallscale fluctuations are shown to be universal.
 Publication:

Proceedings of the 31st International Symposium on Lattice Field Theory (LATTICE 2013). 29 July3 August
 Pub Date:
 2013
 DOI:
 10.22323/1.187.0054
 arXiv:
 arXiv:1311.4386
 Bibcode:
 2013slft.confE..54M
 Keywords:

 High Energy Physics  Lattice;
 Condensed Matter  Statistical Mechanics;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 7 pages, 2 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July  3 August 2013, Mainz, Germany