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Title: Shocks, Rarefaction Waves, and Current Fluctuations for Anharmonic Chains

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. Here, 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.
Authors:
ORCiD logo [1] ;  [2]
  1. Stanford Univ., CA (United States). Geballe Lab. for Advanced Materials; SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES)
  2. Technische Univ. Munchen, Garching (Germany). Zentrum Mathematik and Physik Dept.
Publication Date:
Grant/Contract Number:
AC02-76SF00515
Type:
Accepted Manuscript
Journal Name:
Journal of Statistical Physics
Additional Journal Information:
Journal Volume: 166; Journal Issue: 3-4; Journal ID: ISSN 0022-4715
Publisher:
Springer
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE; Alexander von Humboldt Foundation
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Fluid dynamics; Hydrodynamic waves; Statistical mechanics of classical fluids; Nonequilibrium thermodynamics
OSTI Identifier:
1353110

Mendl, Christian B., and Spohn, Herbert. Shocks, Rarefaction Waves, and Current Fluctuations for Anharmonic Chains. United States: N. p., Web. doi:10.1007/s10955-016-1626-5.
Mendl, Christian B., & Spohn, Herbert. Shocks, Rarefaction Waves, and Current Fluctuations for Anharmonic Chains. United States. doi:10.1007/s10955-016-1626-5.
Mendl, Christian B., and Spohn, Herbert. 2016. "Shocks, Rarefaction Waves, and Current Fluctuations for Anharmonic Chains". United States. doi:10.1007/s10955-016-1626-5. https://www.osti.gov/servlets/purl/1353110.
@article{osti_1353110,
title = {Shocks, Rarefaction Waves, and Current Fluctuations for Anharmonic Chains},
author = {Mendl, Christian B. and Spohn, Herbert},
abstractNote = {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. Here, 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 t1/3 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.},
doi = {10.1007/s10955-016-1626-5},
journal = {Journal of Statistical Physics},
number = 3-4,
volume = 166,
place = {United States},
year = {2016},
month = {10}
}