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Updated: Jul 11, 2026

Characterization of Thermal Transport in One-dimensional Solid Materials
05:20

Characterization of Thermal Transport in One-dimensional Solid Materials

Published on: January 26, 2014

Anomalous thermal conduction in one dimension: a quantum calculation.

G Santhosh1, Deepak Kumar

  • 1School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
PubMed
Summary
This summary is machine-generated.

We investigated thermal conductivity in quantum anharmonic chains. Our findings confirm the exponent alpha=0.4 for thermal conductivity divergence with chain length, supporting previous classical models.

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Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Quantum dynamics

Background:

  • Thermal conductivity in anharmonic chains is crucial for understanding heat transport.
  • Previous studies on classical chains yielded conflicting exponents for conductivity divergence with chain length.
  • The role of quantum effects and quartic anisotropy in this phenomenon requires further investigation.

Purpose of the Study:

  • To investigate the thermal conductivity of a quantum anharmonic chain with quartic anisotropy.
  • To analytically determine the exponent governing the divergence of thermal conductivity with chain length.
  • To explore the influence of quantum mechanics and umklapp scattering on heat transport.

Main Methods:

  • Development of a low-temperature expansion for the relaxation rate gamma(q) of normal modes.
  • Analysis of relaxation mechanisms, specifically umklapp scattering processes.
  • Evaluation of thermal conductivity using the Kubo formula, including vertex corrections.

Main Results:

  • The relaxation rate gamma(q) was found to be proportional to q(5/3)T2 in the low-temperature regime.
  • Umklapp scattering processes were identified as the primary cause of relaxation.
  • The thermal conductivity exponent was calculated to be alpha = 0.4, consistent with earlier classical models.

Conclusions:

  • Quantum anharmonic chains exhibit a thermal conductivity exponent of alpha = 0.4.
  • The low-temperature behavior of relaxation rates is well-described by the derived expansion.
  • The study reconciles findings between classical and quantum models for heat transport in these systems.