Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain

Suman G. Das, Abhishek Dhar, Keiji Saito, Christian B. Mendl, and Herbert Spohn
Phys. Rev. E 90, 012124 – Published 23 July 2014

Abstract

Recent work has developed a nonlinear hydrodynamic fluctuation theory for a chain of coupled anharmonic oscillators governing the conserved fields, namely, stretch, momentum, and energy. The linear theory yields two propagating sound modes and one diffusing heat mode, all three with diffusive broadening. In contrast, the nonlinear theory predicts that, at long times, the sound mode correlations satisfy Kardar-Parisi-Zhang scaling, while the heat mode correlations have Lévy-walk scaling. In the present contribution we report on molecular dynamics simulations of Fermi-Pasta-Ulam chains to compute various spatiotemporal correlation functions and compare them with the predictions of the theory. We obtain very good agreement in many cases, but also some deviations.

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  • Received 16 May 2014

DOI:https://doi.org/10.1103/PhysRevE.90.012124

©2014 American Physical Society

Authors & Affiliations

Suman G. Das*

  • Raman Research Institute, CV Raman Avenue, Sadashivanagar, Bangalore 560080, India

Abhishek Dhar

  • International Center for Theoretical Sciences, TIFR, IISC Campus, Bangalore 560012, India

Keiji Saito

  • Department of Physics, Keio University, Yokohama 223-8522, Japan

Christian B. Mendl§

  • Zentrum Mathematik, TU München, Boltzmannstraße 3, 85747 Garching, Germany

Herbert Spohn

  • Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA

  • *suman@rri.res.in
  • abhishek.dhar@icts.res.in
  • saitoh@rk.phys.keio.ac.jp
  • §mendl@ma.tum.de
  • spohn@ma.tum.de

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Issue

Vol. 90, Iss. 1 — July 2014

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