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New equipartition results for normal mode energies of anharmonic chains


The canonical and microcanonical distributions of energy among the normal modes of an anharmonic chain with nearest-neighbor interactions and free ends are examined. If the interparticle potential is an even function, then energy is distributed uniformly among the normal modes at all energy densities. If the interparticle potential is not an even function but includes quadratic, cubic, and quartic terms, then the energy sharing among the normal modes is also uniform in both the small- and large-energy density limits. At large energies, in this latter case the energy per normal mode scales as the square root of the energy density. Thus we find equipartition of energy among the normal modes of an anharmonic chain. The sum of the normal mode energies is less than the total energy of the chain.

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Henry, B.I., Szeredi, T. New equipartition results for normal mode energies of anharmonic chains. J Stat Phys 78, 1039–1053 (1995). https://doi.org/10.1007/BF02183700

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Key Words

  • Equipartition of energy
  • ergodic hypothesis
  • anharmonic chains
  • normal modes
  • nonlinear lattice dynamics