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Characterization of Thermal Transport in One-dimensional Solid Materials
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Anomalous heat diffusion.

Sha Liu1, Peter Hänggi2, Nianbei Li3

  • 1Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117546 Singapore and NUS Graduate School for Integrative Sciences and Engineering, 117456 Singapore.

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This study reveals that anomalous energy spread in solids is linked to heat flux. The findings establish a connection between energy diffusion and anomalous thermal conductivity scaling.

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Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Thermodynamics

Background:

  • Anomalous energy spread in solids (<Δx(2)(t)>E) arises from non-equilibrium excess energy distributions.
  • Understanding the dynamics of this spread is crucial for predicting material properties.

Purpose of the Study:

  • To investigate the relationship between anomalous energy spread and heat transport in solids.
  • To derive a rigorous connection between energy diffusion and thermal conductivity scaling.

Main Methods:

  • Analysis of the second derivative of the variance of the non-equilibrium excess energy distribution.
  • Relating this to the thermal equilibrium total heat flux autocorrelation function (CJJ(t)).
  • Utilizing a time-local Helfand-like relation.

Main Results:

  • A rigorous relation was derived: d(2)<Δx(2)(t)>E/dt2=2CJJ(t)/(kBT(2)c).
  • The integral of this relation shows a time-local Helfand-like behavior.
  • Anomalous energy diffusion was shown to dictate anomalous thermal conductivity scaling.

Conclusions:

  • The study provides a fundamental link between microscopic energy dynamics and macroscopic thermal transport.
  • This work offers insights into anomalous thermal conductivity in non-equilibrium systems.
  • The derived relation can be a basis for further theoretical and experimental investigations.