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Thermal conductivity and bulk viscosity in quartic oscillator chains.

G R Lee-Dadswell1, B G Nickel, C G Gray

  • 1Department of Physics, University of Guelph, Guelph, Ontario, Canada, N1G 2W1. dadswell@physics.uoguelph.ca

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
Summary

We developed a new theory relating low-frequency thermal conductivity to higher-frequency properties in 1D systems, assuming sound waves dominate heat transport. Simulations confirm this theory, observing a predicted energy spectrum divergence.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Understanding thermal conductivity in low-dimensional systems is crucial for materials science.
  • Previous simulations have not observed the predicted low-frequency behavior of thermal conductivity.

Purpose of the Study:

  • To propose and validate a theoretical relation for predicting low-frequency thermal conductivity in 1D systems.
  • To investigate the role of sound wave propagation in heat transport.

Main Methods:

  • Theoretical modeling based on ballistic transport by sound waves.
  • Molecular dynamics simulations of a 1D particle chain with quartic potentials.
  • Analysis of energy current power spectrum and bulk viscosity.

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Main Results:

  • A simple relation is derived for systems with equal heat capacities (c(p) = c(v)).
  • Simulations of long chains over extended times reveal a crossover into the predicted low-frequency regime.
  • The energy current power spectrum diverges as omega(-1/2) as frequency approaches zero.
  • Simulated bulk viscosity is finite, while thermal conductivity is infinite.

Conclusions:

  • The proposed theory accurately predicts low-frequency thermal conductivity in 1D systems.
  • Ballistic transport by sound waves is confirmed as the dominant heat transport mechanism.
  • The study resolves discrepancies with previous simulations by observing the predicted crossover regime.