English

Energy Transport in Weakly Anharmonic Chains

Statistical Mechanics 2007-05-23 v2 Mathematical Physics math.MP Chaotic Dynamics

Abstract

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.

Keywords

Cite

@article{arxiv.cond-mat/0602082,
  title  = {Energy Transport in Weakly Anharmonic Chains},
  author = {Kenichiro Aoki and Jani Lukkarinen and Herbert Spohn},
  journal= {arXiv preprint arXiv:cond-mat/0602082},
  year   = {2007}
}

Comments

25 pages, 10 figures

R2 v1 2026-07-22T11:28:15.986Z