hal-00280839, version 2

Energy transport in stochastically perturbed lattice dynamics

Giada Basile ¹, Stefano Olla () ², Herbert Spohn () ³

Archive for Rational Mechanics and Analysis 195, 1 (2009) 171-203

• 1:  Weierstrass Institut for Applied Mathematics and Stochastics (WIAS)
• http://www.wias-berlin.de/
  WIAS Mohrenstr. 39 10117 Berlin Germany
• 2:  CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
• http://www.ceremade.dauphine.fr/index.html
  CNRS : UMR7534 – Université Paris IX - Paris Dauphine Place du Maréchal de Lattre de Tassigny 75775 - Paris Cedex 16 France
• 3:  Centre fo Mathematical Sciences (D-MUTU-ZM)
• http://www.ma.tum.de
  Technische Universität München Zentrum Mathematik der Technischen Universität München Boltzmannstr. 3 D-85747 Garching Germany

Available versions :  v1 (2008-05-20) v2 (2008-09-12)

Bibliographic reference

• Type of document: Articles in peer-reviewed journal
• Subject:

  Mathematics/Probability

  Mathematics/Mathematical Physics

  Physics/Mathematical Physics

  Physics/Condensed Matter/Statistical Mechanics

• Title: Energy transport in stochastically perturbed lattice dynamics
• Abstract: We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order ε−1 the local spectral density (Wigner function) evolves according to a linear transport equation describing inelastic collisions. For an energy and momentum conserving chain the transport equation predicts a slow decay, as 1/√t, for the energy current correlation in equilibrium. This is in agreement with previous studies using a different method.
• Fulltext language: English
• DOI: 10.1007/s00205-008-0205-6
• Journal:

  Archive for Rational Mechanics and Analysis
  Publisher	Springer Verlag (Germany)
  ISSN	0003-9527 (eISSN : 1432-0673)

• Audience: international
• Publication date: 2009
• Volume: 195
• Issue: 1
• Page, identifiant, ...: 171-203
• Keyword(s): Wigner functions – semiclassical limits – lattice dynamics – conservative stochastic dynamics – phonon Boltzmann equation – energy transport
• Classification: 82C21; 82C70; 82C31
• ANR Project:

  Project Id

  ANR LHMSHE n.BLAN07-2184264

Attached file list to this document: 

• hal-00280839, version 2
• http://hal.archives-ouvertes.fr/hal-00280839
• oai:hal.archives-ouvertes.fr:hal-00280839
• From: Stefano Olla <>
• Submitted on: Friday, 12 September 2008 14:42:05
• Updated on: Thursday, 25 November 2010 19:03:02