We address the issue of how disorder together with nonlinearity affect energy relaxation in the latticeφ~4 system.The absence of nonlinearity leads such a model to only supporting fully localized Anderson modes whose...We address the issue of how disorder together with nonlinearity affect energy relaxation in the latticeφ~4 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.展开更多
基金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)the Start-up Fund from Jiangxi Science and Technology Normal University(Grant No.2017BSD002)。
文摘We address the issue of how disorder together with nonlinearity affect energy relaxation in the latticeφ~4 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.
