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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 (0αα≠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 x2(t)> is different from anomalous diffusion (i.e. x2(t)> ∝ tα (0αα≠1)), which is produced 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.
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Keywords:
- thermal noise /
- non-Markovian diffusion /
- generalized Langevin equation /
- correlation
[1] Bao J D 2005 Progress Phys. 25 359 (in Chinese) [包景东 2005 物理学进展 25 359]
[2] Zhuo Y Z 2004 Nuclear Phys. Rev. 21 83 (in Chinese) [卓益忠 2004 原子核物理评论 21 83]
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[5] Siegle P, Goychuk I, Hänggi P 2010 Phys. Rev. Lett. 105 100602
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[7] Viñales A D, Despósito M A 2006 Phys. Rev. E 73 016111
[8] Bao J D, Bai Z W 2005 Chin. Phys. Lett. 22 1845
[9] Bao J D, Zhuo Y Z 2003 Phys. Rev. Lett. 91 138104
[10] Siegle P, Goychuk I, Talkner P, Hänggi P 2010 Phys. Rev. E 81 011136
[11] Bao J D 2004 J. Stat. Phys. 114 503
[12] Wang K G 1992 Phys. Rev. A 45 833
[13] Bao J D, Song Y L, Ji Q, Zhuo Y Z 2005 Phys. Rev. E 72 011113
[14] Bao J D, Zhuo Y Z, Oliveira F A, Hänggi P 2006 Phys. Rev. E 74 061111
[15] Viñales A D, Wang K G, Despósito M A 2009 Phys. Rev. E 80 011101
[16] L K, Bao J D 2005 Phys. Rev. E 72 067701
[17] Plyukhin A V 2011 Phys. Rev. E 83 062102
[18] Neiman A, Sung W 1996 Phys. Lett. A 223 341
[19] Bai W S M, Peng H, Tu Z, Ma H 2012 Acta Phys. Sin. 61 210501 (in Chinese) [白文斯密, 彭皓, 屠浙, 马洪 2012 61 210501]
[20] Zhong S C, Gao S L, Wei K, Ma H 2012 Acta Phys. Sin. 61 170501 (in Chinese) [钟苏川, 高仕龙, 韦鹍, 马洪 2012 61 170501]
[21] Xu W, Jin Y F, Xu M, Li W 2005 Acta Phys. Sin. 54 5027 (in Chinese) [徐伟, 靳艳飞, 徐猛, 李伟 2005 54 5027]
[22] Jin Y F, Hu H Y 2009 Acta Phys. Sin. 58 2895 (in Chinese) [靳艳飞, 胡海岩 2009 58 2895]
[23] Jin Y F 2012 Physica A 391 1928
[24] Zeng C H, Wang H, Wang H T 2011 Chin. Phys. B 20 050502
[25] Fuliński A, Telejko T 1991 Phys. Lett. A 152 11
[26] Zhang N M, Xu W, Wang C Q 2007 Acta Phys. Sin. 56 5083 (in Chinese) [张娜敏, 徐伟, 王朝庆 2007 56 5083]
[27] Jiang L L, Luo X Q, Wu D, Zhu S Q 2012 Chin. Phys. B 21 090503
[28] Wang Y X, Zhao N R, Yan Y J 2012 Phys. Rev. E 85 041142
[29] Roy D, Kumar N 2008 Phys. Rev. E 78 052102
[30] Kumar N 2012 Phys. Rev. E 85 011114
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[1] Bao J D 2005 Progress Phys. 25 359 (in Chinese) [包景东 2005 物理学进展 25 359]
[2] Zhuo Y Z 2004 Nuclear Phys. Rev. 21 83 (in Chinese) [卓益忠 2004 原子核物理评论 21 83]
[3] Wang K G, Tokuyama M 1999 Physica A 265 341
[4] Bao J D, Zhou Y, L K 2006 Phys. Rev. E 74 041125
[5] Siegle P, Goychuk I, Hänggi P 2010 Phys. Rev. Lett. 105 100602
[6] Porrá J M, Wang K G, Masoliver J 1996 Phys. Rev. E 53 5872
[7] Viñales A D, Despósito M A 2006 Phys. Rev. E 73 016111
[8] Bao J D, Bai Z W 2005 Chin. Phys. Lett. 22 1845
[9] Bao J D, Zhuo Y Z 2003 Phys. Rev. Lett. 91 138104
[10] Siegle P, Goychuk I, Talkner P, Hänggi P 2010 Phys. Rev. E 81 011136
[11] Bao J D 2004 J. Stat. Phys. 114 503
[12] Wang K G 1992 Phys. Rev. A 45 833
[13] Bao J D, Song Y L, Ji Q, Zhuo Y Z 2005 Phys. Rev. E 72 011113
[14] Bao J D, Zhuo Y Z, Oliveira F A, Hänggi P 2006 Phys. Rev. E 74 061111
[15] Viñales A D, Wang K G, Despósito M A 2009 Phys. Rev. E 80 011101
[16] L K, Bao J D 2005 Phys. Rev. E 72 067701
[17] Plyukhin A V 2011 Phys. Rev. E 83 062102
[18] Neiman A, Sung W 1996 Phys. Lett. A 223 341
[19] Bai W S M, Peng H, Tu Z, Ma H 2012 Acta Phys. Sin. 61 210501 (in Chinese) [白文斯密, 彭皓, 屠浙, 马洪 2012 61 210501]
[20] Zhong S C, Gao S L, Wei K, Ma H 2012 Acta Phys. Sin. 61 170501 (in Chinese) [钟苏川, 高仕龙, 韦鹍, 马洪 2012 61 170501]
[21] Xu W, Jin Y F, Xu M, Li W 2005 Acta Phys. Sin. 54 5027 (in Chinese) [徐伟, 靳艳飞, 徐猛, 李伟 2005 54 5027]
[22] Jin Y F, Hu H Y 2009 Acta Phys. Sin. 58 2895 (in Chinese) [靳艳飞, 胡海岩 2009 58 2895]
[23] Jin Y F 2012 Physica A 391 1928
[24] Zeng C H, Wang H, Wang H T 2011 Chin. Phys. B 20 050502
[25] Fuliński A, Telejko T 1991 Phys. Lett. A 152 11
[26] Zhang N M, Xu W, Wang C Q 2007 Acta Phys. Sin. 56 5083 (in Chinese) [张娜敏, 徐伟, 王朝庆 2007 56 5083]
[27] Jiang L L, Luo X Q, Wu D, Zhu S Q 2012 Chin. Phys. B 21 090503
[28] Wang Y X, Zhao N R, Yan Y J 2012 Phys. Rev. E 85 041142
[29] Roy D, Kumar N 2008 Phys. Rev. E 78 052102
[30] Kumar N 2012 Phys. Rev. E 85 011114
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