Controlling the size scaling of the thermal conductivity in harmonic chains with correlated mass disorder

Author(s)

Herrera-Gonzalez, I. F. ^[1] ; Mendez-Bermudez, J. A. ^{[2, 3]}

Affiliation

^[1] Univ Popular Autonoma Estado Puebla, Dept Ingn, Puebla 72410, Pue - Mexico

^[2] Benemerita Univ Autonoma Puebla, Inst Fis, Apartado Postal J-48, Puebla 72570 - Mexico

^[3] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat Aplicada & Estat, Campus Sao Carlos, Caixa Postal 668, Sao Carlos 13560970, SP - Brazil

• Document type: Journal article
• Source: Physics Letters A; v. 384, n. 18 JUN 26 2020.
• Web of Science Citations: 0

Abstract

We address the general problem of heat conduction in one dimensional harmonic chains, with correlated isotopic disorder, attached at their ends to white noise or Rubin's model of heat baths. The scaling behavior of the thermal conductivity is independent of the heat reservoirs, but depends on the boundary conditions and the low wave-number mu behavior of the power spectrum W(mu) of the fluctuations of the random masses around their common mean value. Thus, by properly tuning W(mu) we are able to control the scaling of the thermal conductivity kappa with the system size N. As an example, we show that if W(mu) similar to exp(-1/mu)/mu(2), then kappa similar to N/(logN)(3) for fixed boundary conditions and kappa similar to N/log(N) for free boundary conditions, which represent non-standard scalings of the thermal conductivity. In addition, we obtain the asymptotic dependence of the thermal conductivity on the coupling strength between the harmonic chain and the heat baths. (C) 2020 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 19/06931-2 - Random matrix theory approach to complex networks
• Grantee: Francisco Aparecido Rodrigues
• Support Opportunities: Research Grants - Visiting Researcher Grant - International