2019/11/01 by I. F. Herrera-González, I. F. Herrera-Gonzalez, Herrera-Gonzalez, I. F. +3
Materials Science · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Material Dynamics and Properties #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1911.00592
9 pages, 7 figures
arxiv created 2019/11/01 · openalex publication_date 2019/11/01 · arxiv updated 2019/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider heat transport in one-dimensional harmonic chains attached at its ends to Langevin heat baths. The harmonic chain has mass impurities where the separation d between any two successive impurities is randomly distributed according to a power-law distribution P(d)∼ 1/dα+1, being α>0. In the regime where the first moment of the distribution is well defined (1<α<2) the thermal conductivity κ scales with the system size N as κ∼ N(α-3)/α for fixed boundary conditions, whereas for free boundary conditions κ∼ N(α-1)/α if N≫1. When α=2, the inverse localization length λ scales with the frequency ω as λ∼ ω2 ln ω in the low frequency regime, due to the logarithmic correction, the size scaling law of the thermal conductivity acquires a non-closed form. When α>2, the thermal conductivity scales as in the uncorrelated disorder case. The situation α<1 is only analyzed numerically, where λ(ω)∼ ω2-α which leads to the following asymptotic thermal conductivity: κ∼ N-(α+1)/(2-α) for fixed boundary conditions and κ∼ N(1-α)/(2-α) for free boundary conditions.