Weinberg I, de Leeuw Y, Kottos T, Cohen D. Resistor-network anomalies in the heat transport of random harmonic chains.
Phys Rev E 2016;
93:062138. [PMID:
27415239 DOI:
10.1103/physreve.93.062138]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2016] [Indexed: 11/07/2022]
Abstract
We consider thermal transport in low-dimensional disordered harmonic networks of coupled masses. Utilizing known results regarding Anderson localization, we derive the actual dependence of the thermal conductance G on the length L of the sample. This is required by nanotechnology implementations because for such networks Fourier's law G∝1/L^{α} with α=1 is violated. In particular we consider "glassy" disorder in the coupling constants and find an anomaly which is related by duality to the Lifshitz-tail regime in the standard Anderson model.
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