Thermal conduction in classical low-dimensional lattices

S Lepri, R Livi, A Politi

Research output: Contribution to journalLiterature reviewpeer-review

1225 Citations (Scopus)


Deriving macroscopic phenomenological laws of irreversible thermodynamics from simple microscopic models is one of the tasks of non-equilibrium statistical mechanics. We consider stationary energy transport in crystals with reference to simple mathematical models consisting of coupled oscillators on a lattice. The role of lattice dimensionality on the breakdown of the Fourier's law is discussed and some universal quantitative aspects are emphasized: the divergence of the finite-size thermal conductivity is characterized by universal laws in one and two dimensions. Equilibrium and non-equilibrium molecular dynamics methods are presented along with a critical survey of previous numerical results. Analytical results for the non-equilibrium dynamics can be obtained in the harmonic chain where the role of disorder and localization can be also understood. The traditional kinetic approach, based on the Boltzmann-Peierls equation is also briefly sketched with reference to one-dimensional chains. Simple toy models can be defined in which the conductivity is finite. Anomalous transport in integrable non-linear systems is briefly discussed. Finally, possible future research themes are outlined. (C) 2002 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)1-80
Number of pages80
JournalPhysics Reports
Issue number1
Publication statusPublished - Apr 2003


  • thermal conductivity
  • classical lattices
  • nonequilibrium molecular-dynamics
  • disordered harmonic chain
  • diatomic toda lattice
  • heat-conduction
  • energy-transport
  • statistical-mechanics
  • Hamiltonian-systems
  • anharmonic chains
  • Fouriers Law
  • XY-model


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