Energy transport in weakly anharmonic chains

Kenichiro Aoki, Jani Lukkarinen, Herbert Spohn

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular coupling parameters before, and confirmed by our study, such chains satisfy Fourier's law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level we employ the Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for a finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations. In the range of weak anharmonicity, respectively low temperatures, reasonable agreement is observed.

Original languageEnglish
Pages (from-to)1105-1129
Number of pages25
JournalJournal of Statistical Physics
Issue number5
Publication statusPublished - 2006 Sept


  • Fourier's law
  • Molecular dynamics
  • One-dimensional lattice dynamics
  • Phonon Boltzmann equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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