Energy relaxation in disordered lattice φ4 system: The combined effects of disorder and nonlinearity

doi:10.1088/1674-1056/abc15b

Abstract We address the issue of how disorder together with nonlinearity affect energy relaxation in the lattice φ⁴ system. The absence of nonlinearity leads such a model to only supporting fully localized Anderson modes whose energies will not relax. However, through exploring the time decay behavior of each Anderson mode's energy-energy correlation, we find that adding nonlinearity, three distinct relaxation details can occur. (i) A small amount of nonlinearity causes a rapid exponential decay of the correlation for all modes. (ii) In the intermediate value of nonlinearity, this exponential decay will turn to power-law with a large scaling exponent close to -1. (iii) Finally, all Anderson modes' energies decay in a power-law manner but with a quite small exponent, indicating a slow long-time tail decay. Obviously, the last two relaxation details support a new localization mechanism. As an application, we show that these are relevant to the nonmonotonous nonlinearity dependence of thermal conductivity. Our results thus provide new information for understanding the combined effects of disorder and nonlinearity on energy relaxation.

Keywords: classical transport localized modes Anderson localization

Received: 11 August 2020
Revised: 22 September 2020
Accepted manuscript online: 15 October 2020

PACS:	05.60.Cd	(Classical transport)
	63.20.Pw	(Localized modes)
	66.70.-f	(Nonelectronic thermal conduction and heat-pulse propagation in solids;thermal waves)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11847015, 11975190, 11575046, and 11964012), the Natural Science Foundation of Fujian Province, China (Grant No. 2017J06002), and the Start-up Fund from Jiangxi Science and Technology Normal University (Grant No. 2017BSD002).

Corresponding Authors: ^†Corresponding author. E-mail: xmuxdx@163.com

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Jianjin Wang(汪剑津), Yong Zhang(张勇), and Daxing Xiong(熊大兴) Energy relaxation in disordered lattice φ⁴ system: The combined effects of disorder and nonlinearity 2020 Chin. Phys. B 29 120503

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Energy relaxation in disordered lattice φ4 system: The combined effects of disorder and nonlinearity

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Energy relaxation in disordered lattice φ⁴ system: The combined effects of disorder and nonlinearity