随机双指数记忆耗散系统的非马尔可夫扩散  

Non-Markovian diffusion of the stochastic system with a biexponentical dissipative memory kernel

作　　者：谢文贤[1] 许鹏飞[1] 蔡力[1] 李东平[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《物理学报》2013年第8期19-24,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11101333);陕西省自然科学基金(批准号:2011GQ1018);西北工业大学基础研究基金(批准号:JC201152)资助的课题~~

摘　　要：针对具有双指数耗散记忆核函数的两自由度耦合系统,本文利用Laplace变换导出了热宽带噪声激励下该系统响应二阶矩的解析表达式,并观察到位移二阶矩不同于单自由度情形下的反常扩散x2(t)∝tα(0<α<2,α=1),而是随时间及噪声等参数变化呈现普遍的振荡扩散现象.分析可得,阻尼耦合因子B使粒子远离简谐势场的束缚,x2(t)随B的增大扩散加剧,而摩擦系数增大却使其趋于平稳状态.进一步,若两热噪声互关联时,较小的互关联时间对二阶矩的影响较大,反之作用较小.伴随互关联强度递增,位移二阶矩的扩散加剧,位移间的相关性加强,与物理直观相符.In this paper, second-moments of the responses are analytically solved by the Laplace transform in a coupling two-degree-of- freedom system with a biexponentical dissipative memory kernel function driven by a thermal broadband noise. The mean square displacement 〈x^2（t）〉 is different from anomalous diffusion （i.e. 〈x^2（t）〉∝t^α（0〈α〈2,α=1））, which is induced by the single- degree-of-freedom generalized Langevin equation. The oscillation-diffusion of 〈x^2（t）〉 with the change of time and noise parameters is observed generally. According to our analysis, a particle confined by the harmonic potential can escape with the help of the coupling-damping factor B. The diffusion of 〈x^2（t）〉 aggravates with B increasing. However, 〈x^2（t）〉 tends to the stationary state with the increase of the friction coefficient. Further, if the two thermal noises are in cross-correlation, smaller cross-correlation time has a deeper influence on second-moments. Meanwhile, the diffusion aggravates and the cross-correlation between two displacements strengthens markedly with cross-correlation strength increasing. It is consistent with physical intuition.

关 键 词：热噪声 非马尔可夫扩散 广义朗之万方程 关联性 

分 类 号：O415.3[理学—理论物理]