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
Rectification phenomena and the phase locking in a two-dimensional overdamped Frenkel-Kontorova model with a graphite periodic substrate were studied. The presence of dc and ac forces in the longitudinal direction cau...Rectification phenomena and the phase locking in a two-dimensional overdamped Frenkel-Kontorova model with a graphite periodic substrate were studied. The presence of dc and ac forces in the longitudinal direction causes the appearance of dynamicalmode locking and the steps in the response function of the system. On the other hand, the presence of an ac force in the transverse direction causes the appearance of rectification,even though there is no net dc force in the transverse direction. It is found that whereas the longitudinal velocity increases in a series of steps, rectification in the transverse direction can occur only between two neighbor steps. The amplitude and phase of the external ac driving force affect the depinning force,rectification of the system and particles trajectories.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.
文摘Rectification phenomena and the phase locking in a two-dimensional overdamped Frenkel-Kontorova model with a graphite periodic substrate were studied. The presence of dc and ac forces in the longitudinal direction causes the appearance of dynamicalmode locking and the steps in the response function of the system. On the other hand, the presence of an ac force in the transverse direction causes the appearance of rectification,even though there is no net dc force in the transverse direction. It is found that whereas the longitudinal velocity increases in a series of steps, rectification in the transverse direction can occur only between two neighbor steps. The amplitude and phase of the external ac driving force affect the depinning force,rectification of the system and particles trajectories.
