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Heat conduction in harmonic chains with Lévy-type disorder.

I F Herrera-González1, J A Méndez-Bermúdez2

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Summary
This summary is machine-generated.

This study investigates heat transport in harmonic chains with random mass impurities. Thermal conductivity depends on impurity distribution and system size, revealing complex scaling laws for different disorder regimes.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Disordered Systems

Background:

  • Heat transport in low-dimensional systems is crucial for understanding thermal properties.
  • Disorder significantly impacts thermal conductivity, often leading to localization.
  • Harmonic chains with mass impurities provide a fundamental model for studying these effects.

Purpose of the Study:

  • To analyze heat transport in a 1D harmonic chain with power-law distributed mass impurities.
  • To determine the scaling laws of thermal conductivity with system size (N) for various disorder strengths (α).
  • To investigate the influence of boundary conditions (fixed vs. free) on thermal transport.

Main Methods:

  • Theoretical analysis of heat transport using Langevin heat baths.
  • Derivation of scaling laws for thermal conductivity (κ) based on system size (N) and disorder parameter (α).
  • Analysis of inverse localization length (λ) as a function of frequency (ω) for different α values.

Main Results:

  • For 1<α<2, κ scales as N^((α-3)/α) (fixed BC) or N^((α-1)/α) (free BC).
  • For α=2, logarithmic corrections affect thermal conductivity scaling.
  • For α>2, scaling resembles uncorrelated disorder; for α<1, numerical analysis shows κ ~ N^(-(α+1)/(2-α)) (fixed BC) or N^((1-α)/(2-α)) (free BC).

Conclusions:

  • The thermal conductivity of harmonic chains with power-law distributed mass impurities exhibits complex size-dependent scaling.
  • The exponent α governing the impurity distribution critically determines the heat transport behavior.
  • Boundary conditions play a significant role in the asymptotic thermal conductivity.