Small perturbation of a disordered harmonic chain by a noise and an\n anharmonic potential

2011/11/28 by Cédric Bernardin, François Huveneers, Bernardin, Cédric +1
Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Material Dynamics and Properties #Mathematical Physics (math-ph) #Theoretical and Computational Physics #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.1111.6383

openalex publication_date 2011/11/28 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We study the thermal properties of a pinned disordered harmonic chain weakly\nperturbed by a noise and an anharmonic potential. The noise is controlled by a\nparameter \λ \→ 0, and the anharmonicity by a parameter\n\λ' \≤ \λ. Let \κ be the conductivity of the chain, defined\nthrough the Green-Kubo formula. Under suitable hypotheses, we show that \κ\n= mathcal O (\λ) and, in the absence of anharmonic potential, that\n\κ \∼ \λ. This is in sharp contrast with the ordered chain for\nwhich \κ \∼ 1/\λ, and so shows the persitence of localization\neffects for a non-integrable dynamics.\n

Citations

• Toward the Fourier law for a weakly interacting anharmonic crystal

Related

• Thermal conductivity for a chain of anharmonic oscillators perturbed by a conservative noise
• Asymptotic localization of energy in non-disordered oscillator chains
• Long persistence of localization in a disordered anharmonic chain beyond the atomic limit
• Non-standard anomalous heat conduction in harmonic chains with correlated isotopic disorder
• Recovery of normal heat conduction in harmonic chains with correlated disorder