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Heat transport and current fluctuations in harmonic crystals

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  • Dhar, Abhishek
  • Dandekar, Rahul

Abstract

The approach of studying heat conduction in harmonic crystals, using generalized Langevin equations and phonon Green’s functions, is explained in this review. We present the detailed derivation of the Landauer formula for phonon heat transfer using this approach. Some applications of the Landauer formula to understanding heat conduction in one-dimensional ordered and mass-disordered harmonic chains are given. It is explained how different boundary conditions lead to completely different system-size dependence of the average current in disordered chains. Finally we discuss the fluctuations in the total heat transferred in a fixed large interval of time and show how the Langevin approach is also useful in computing properties of these fluctuations in a harmonic system. In particular we derive the general formula for the cumulant generating function of these fluctuations.

Suggested Citation

  • Dhar, Abhishek & Dandekar, Rahul, 2015. "Heat transport and current fluctuations in harmonic crystals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 418(C), pages 49-64.
    • Handle: RePEc:eee:phsmap:v:418:y:2015:i:c:p:49-64
    DOI: 10.1016/j.physa.2014.06.002
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    Cited by:

    1. Liu, Yong-Yang & Xu, Yu-Liang & Liu, Zhong-Qiang & Li, Jing & Wang, Chun-Yang & Kong, Xiang-Mu, 2018. "Effects of geometrical structure on spatial distribution of thermal energy in two-dimensional triangular lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 185-194.

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