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Additivity principle in high-dimensional deterministic systems.

Keiji Saito1, Abhishek Dhar

  • 1Raman Research Institute, Bangalore 560080, India.

Physical Review Letters
|January 17, 2012
PubMed
Summary
This summary is machine-generated.

The additivity principle accurately describes heat conduction in 3D disordered harmonic lattices across diffusive and anomalous regimes. Three dimensionality is crucial for its validity in these complex transport systems.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Transport Phenomena

Background:

  • The additivity principle (AP) offers a conjecture for heat transfer in complex systems.
  • Understanding heat conduction in disordered systems is crucial for materials science.
  • Deterministic dynamics and dimensionality influence transport properties.

Purpose of the Study:

  • To investigate the validity of the additivity principle (AP) for heat conduction.
  • To analyze heat transfer in three-dimensional disordered harmonic lattices.
  • To explore the effects of dimensionality and transport regimes on the AP.

Main Methods:

  • Accurate calculation of the cumulant generating function (CGF) for heat transfer.
  • Comparison of calculated CGF with the one predicted by the AP.
  • Analysis of heat conduction in ballistic, diffusive, and anomalous transport regimes.

Main Results:

  • The AP shows clear agreement with the CGF in the diffusive regime, even in high dimensions.
  • Surprisingly, the AP also provides a good fit for the CGF in the anomalous transport regime.
  • The importance of three dimensionality for the AP's validity is highlighted.

Conclusions:

  • The additivity principle is a robust descriptor for heat conduction in 3D disordered harmonic lattices.
  • The AP's applicability extends beyond the diffusive regime to anomalous transport.
  • Future studies should consider the role of dimensionality in heat transport phenomena.