CAJ | 학술논문

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.
침대구유쌍지수모산기억핵함수적량자유도우합계통,본문이용Laplace변환도출료열관대조성격려하해계통향응이계구적해석표체식,병관찰도위이이계구불동우단자유도정형하적반상확산?x2(t)?∝tα(0<α<2,α=1),이시수시간급조성등삼수변화정현보편적진탕확산현상.분석가득,조니우합인자B사입자원리간해세장적속박,?x2(t)?수B적증대확산가극,이마찰계수증대각사기추우평은상태.진일보,약량열조성호관련시,교소적호관련시간대이계구적영향교대,반지작용교소.반수호관련강도체증,위이이계구적확산가극,위이간적상관성가강,여물리직관상부.
@@@@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?x2(t)?is different from anomalous diffusion (i.e. ?x2(t)?∝tα (0<α <2, α =1)), which is induced by the single-degree-of-freedom generalized Langevin equation. The oscillation-diffusion of?x2(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?x2(t)?aggravates with B increasing. However,?x2(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.