Heat conduction in harmonic chains with Lévy-type disorder.

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.