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用n阶时间导数噪声作为内部热噪声驱动自由粒子运动时, 若该噪声所对应的非各态历经强度b≠0, 且系统初始处于热平衡, 则此时系统的长时稳态速度可以作为非各态历经噪声使用. 非各态历经噪声具有谱密度在零频处发散的特点, 一维半无界耦合简谐振子链对与之相连的气体分子的作用具有非各态历经噪声的特点, 是非各态历经噪声的实例. 最后将非各态历经噪声作为外噪声驱动倾斜周期势中的粒子运动, 系统出现扩散指数α>2的超弹道扩散现象. 同时发现系统的速度分布将呈现出迁移态和锁定态两种不同状态, 并且处于迁移态的粒子的速度分布为双峰. 迁移态中双峰的出现是一种比较新奇的现象.When using the noise of n-order time derivative as an internal thermal noise to drive a generalized Langevin equation, if the nonergodicty strength of the noise satisfies b ≠ 0 and the system is in thermal equilibrium, then the stationary velocity variable of the system can be used as a non-ergodic noise. The spectra of the non-ergodic noise is infinite at zero frequency. The one-dimensional semi-unbounded coupled harmonic oscillator chains connected with the gas molecules act as the non-ergodic noise, which is an example of non-ergodic noise. Finally regarding the non-ergodic noise as an external noise to drive the particles in the titled periodic potential, it is found that there appears superballistic diffusion with the effective diffusion index exceeding a ballistic value of 2. It is also found that the velocity distribution of the system displays two motion states, the “locked state” and the “running state”. And in the “running state” there occurs a bimodal phenomenon, which is a relatively new phenomenon.
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Keywords:
- non-ergodic noise /
- the noise of n-order time derivative /
- the spectra of the noise /
- superballistic diffusion
[1] Bao J D 2009 Random Simulation Method of Classical and Quantum Dissipation System (Beijing: Science Press) p80 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法 (北京: 科学出版社) 第80页]
[2] Saubamea B, Leduc M, Cohen-Tannoudji C 1999 Phys. Rev. Lett. 83 3796
[3] Brokmann X, Hermier J P, Messin G, Deebiolles P, Bouchard J P, Dahan M 2003 Phys. Rev. Lett. 90 120601
[4] Bao J D, Zhou Y Z 2003 Phys. Rev. Lett. 91 138104
[5] Bao J D, Bai Z W 2005 Chin. Phys. Lett. 22 1845
[6] Leggett A J 1980 Theor. Phys. Suppl. 69 80
[7] Lu H, Qin L, Bao J D 2009 Acta Phys. Sin. 58 8127 (in Chinese) [卢宏, 覃莉, 包景东 2009 58 8127]
[8] Lu H, Bao J D 2013 Chin. Phys. Lett. 30 010502
[9] Reimann P 2002 Phys. Rep. 361 57
[10] Moreira A A, Luís A, Amaral N 2005 Phys. Rev. Lett. 94 218702
[11] Bai Z W, Meng G Q 2008 Acta Phys. Sin. 57 7477 (in Chinese) [白占武, 蒙高庆 2008 57 7477]
[12] Bao J D, Hänggi P, Zhou Y Z 2005 Phys. Rev. E 72 061107
[13] Bao J D, Song Y L, Zhou Y Z 2005 Phys. Rev. E 72 011113
[14] Ford G W, Kac M, Mazur P 1965 J. Math. Phys. 6 504
[15] Ford G W, Lewis J T, O'Connell R F 1988 J. Stat. Phys. 53 439
[16] Ford G W, Lewis J T, O'Connell R F 1988 Phys. Rev. A 37 4419
[17] Rosa J, Beims M W 2008 Phys. Rev. E 78 031126
[18] Zwanzig R W 1960 J. Chem. Phys. 32 1173
[19] Weiss U 1999 Quantum Dissipative Systems (2nd Ed.) (Singapore: World Scientific)
[20] L K, Bao J D 2007 Phys. Rev. E 76 061119
[21] Bao J D, Liu J 2013 Phys. Rev. E 88 022153
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[1] Bao J D 2009 Random Simulation Method of Classical and Quantum Dissipation System (Beijing: Science Press) p80 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法 (北京: 科学出版社) 第80页]
[2] Saubamea B, Leduc M, Cohen-Tannoudji C 1999 Phys. Rev. Lett. 83 3796
[3] Brokmann X, Hermier J P, Messin G, Deebiolles P, Bouchard J P, Dahan M 2003 Phys. Rev. Lett. 90 120601
[4] Bao J D, Zhou Y Z 2003 Phys. Rev. Lett. 91 138104
[5] Bao J D, Bai Z W 2005 Chin. Phys. Lett. 22 1845
[6] Leggett A J 1980 Theor. Phys. Suppl. 69 80
[7] Lu H, Qin L, Bao J D 2009 Acta Phys. Sin. 58 8127 (in Chinese) [卢宏, 覃莉, 包景东 2009 58 8127]
[8] Lu H, Bao J D 2013 Chin. Phys. Lett. 30 010502
[9] Reimann P 2002 Phys. Rep. 361 57
[10] Moreira A A, Luís A, Amaral N 2005 Phys. Rev. Lett. 94 218702
[11] Bai Z W, Meng G Q 2008 Acta Phys. Sin. 57 7477 (in Chinese) [白占武, 蒙高庆 2008 57 7477]
[12] Bao J D, Hänggi P, Zhou Y Z 2005 Phys. Rev. E 72 061107
[13] Bao J D, Song Y L, Zhou Y Z 2005 Phys. Rev. E 72 011113
[14] Ford G W, Kac M, Mazur P 1965 J. Math. Phys. 6 504
[15] Ford G W, Lewis J T, O'Connell R F 1988 J. Stat. Phys. 53 439
[16] Ford G W, Lewis J T, O'Connell R F 1988 Phys. Rev. A 37 4419
[17] Rosa J, Beims M W 2008 Phys. Rev. E 78 031126
[18] Zwanzig R W 1960 J. Chem. Phys. 32 1173
[19] Weiss U 1999 Quantum Dissipative Systems (2nd Ed.) (Singapore: World Scientific)
[20] L K, Bao J D 2007 Phys. Rev. E 76 061119
[21] Bao J D, Liu J 2013 Phys. Rev. E 88 022153
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