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提出一种朗之万动力学方法获取处于热平衡态耦合系统内部振子坐标，数值模拟了单端固定简谐振子链的时间演化行为，并将其平衡性质与解析解进行了比较. 结果表明了朗之万动力学方法的有效性. 推广应用于非简谐四次方型耦合系统，模拟得到振子的四次方均坐标，与理论值验证；以模拟结果作为样本点计算哈密顿量，其能量分布与Boltzmann分布相符.
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关键词:
- 耦合振子链 /
- Langevin方程 /
- 稳态分布
We have studied two probability potentials of a collinear oscillator atom chain and developed a Langevin dynamics approach for calculation. In the case of the harmonic chains, results of the Monte Carlo simulations are compared with the analytical solutions to verify the validity of this approach. In the case of 4-times coupled oscillator chains, the results of numerical simulations are used to the calculation of Hamiltonian. Then the system's energy distribution and the Maxwell-Boltzmann distribution are compared, and found to be in agreement with each other.[1] Zwanzig R W 1960 J. Chem. Phys. 32 1173
[2] [3] McCarroll B, Ehrlich G 1963 J. Chem. Phys. 38 523
[4] Goodman F 1962 J. Chem. Phys. Solid 23 1269
[5] [6] Adelman S A, Brooks C L 1982 J. Chem. Phys. 86 1511
[7] [8] Adelman S A, Doll J D 1974 J. Chem. Phys. 61 4242
[9] [10] [11] Doll J D, Myers L E 1975 J. Chem. Phys. 63 4908
[12] [13] Martens S, Hennig D, Fugmann S, Schimansky-Geier L 2008 Phys. Rev. E 78 041121
[14] Lee M H, Hong J 1985 Phys. Rev. B 32 7734
[15] [16] [17] Tully J C 1980 J. Chem. Phys. 73 1975
[18] [19] Tasic U, Scott Day B, Yan T, Morris J R, Hase W L 2008 J. Phys. Chem. C 112 476
[20] Peng Y X, Liu L, Gao Z, Li S, Mazyar O. A, Hase W L, Yan T Y 2008 J. Phys. Chem. C 112 20340
[21] [22] [23] Nagard M B, Andersson P U, Markovic N, Petterssona J B C 1998 J. Chem. Phys. 109 10339
[24] Shiraishi M, Takenobu T, Ata M 2003 Chem. Phys. Lett. 367 633
[25] [26] [27] Liu J, Wang H Y, Bao J D 2013 Chin. Phys. B 22 060513
[28] Deng W H 2009 Phys. Rev. E 79 011112
[29] [30] Bao J D 2009 Stochastic Simulation Method of Classical and Quantum Dissipative Systems (Beijing: Science Press) p38 (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38页]
[31] -
[1] Zwanzig R W 1960 J. Chem. Phys. 32 1173
[2] [3] McCarroll B, Ehrlich G 1963 J. Chem. Phys. 38 523
[4] Goodman F 1962 J. Chem. Phys. Solid 23 1269
[5] [6] Adelman S A, Brooks C L 1982 J. Chem. Phys. 86 1511
[7] [8] Adelman S A, Doll J D 1974 J. Chem. Phys. 61 4242
[9] [10] [11] Doll J D, Myers L E 1975 J. Chem. Phys. 63 4908
[12] [13] Martens S, Hennig D, Fugmann S, Schimansky-Geier L 2008 Phys. Rev. E 78 041121
[14] Lee M H, Hong J 1985 Phys. Rev. B 32 7734
[15] [16] [17] Tully J C 1980 J. Chem. Phys. 73 1975
[18] [19] Tasic U, Scott Day B, Yan T, Morris J R, Hase W L 2008 J. Phys. Chem. C 112 476
[20] Peng Y X, Liu L, Gao Z, Li S, Mazyar O. A, Hase W L, Yan T Y 2008 J. Phys. Chem. C 112 20340
[21] [22] [23] Nagard M B, Andersson P U, Markovic N, Petterssona J B C 1998 J. Chem. Phys. 109 10339
[24] Shiraishi M, Takenobu T, Ata M 2003 Chem. Phys. Lett. 367 633
[25] [26] [27] Liu J, Wang H Y, Bao J D 2013 Chin. Phys. B 22 060513
[28] Deng W H 2009 Phys. Rev. E 79 011112
[29] [30] Bao J D 2009 Stochastic Simulation Method of Classical and Quantum Dissipative Systems (Beijing: Science Press) p38 (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38页]
[31]
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