Shocks,Rarefaction Waves,and Current Fluctuations for Anharmonic Chains |
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| Authors: | Christian B Mendl Herbert Spohn |
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| Institution: | 1.Geballe Laboratory for Advanced Materials,Stanford University,Stanford,USA;2.Stanford Institute for Materials and Energy Sciences,SLAC National Accelerator Laboratory,Menlo Park,USA;3.Zentrum Mathematik and Physik Department,Technische Universit?t München,Garching bei München,Germany |
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| Abstract: | The nonequilibrium dynamics of anharmonic chains is studied by imposing an initial domain-wall state, in which the two half lattices are prepared in equilibrium with distinct parameters. We analyse the Riemann problem for the corresponding Euler equations and, in specific cases, compare with molecular dynamics. Additionally, the fluctuations of time-integrated currents are investigated. In analogy with the KPZ equation, their typical fluctuations should be of size \(t^{1/3}\) and have a Tracy–Widom GUE distributed amplitude. The proper extension to anharmonic chains is explained and tested through molecular dynamics. Our results are calibrated against the stochastic LeRoux lattice gas. |
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