Derivation of diffusion coefficient of a Brownian particle in tilted periodic potential from the coordinate moments. (English) Zbl 1231.82051
Summary: The diffusion of an overdamped Brownian particle in the tilted periodic potential is investigated. Using the one-dimensional hopping model, the formulations of the mean velocity \(V_N\) and effective diffusion coefficient \(D_N\) of the Brownian particle have been obtained [B. Derrida, J. Stat. Phys. 31, No. 3, 433-450 (1983) ]. Based on the relation between the effective diffusion coefficient and the moments of the mean first passage time, the formulation of effective diffusion coefficient Deff of the Brownian particle also has been obtained [P. Reimann et al., Phys. Rev. E 65 No. 3, article No. 031104 (2002)]. In this research, we’ll give another analytical expression of the effective diffusion coefficient Deff from the moments of the particle’s coordinate.
MSC:
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
| 82C24 | Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics |
| 60J65 | Brownian motion |
References:
| [1] | Barone, A.; Paterno, G., Physics and Applications of the Josephson Effect (1982), Wiley: Wiley New York |
| [2] | Lindsey, W. C., Synchronization Systems in Communication and Control (1972), Prentice Hall: Prentice Hall Englewood Cliffs, NJ |
| [3] | Rubi, J. M.; Reguera, D.; Pérez-Madrid, A., Phys. Rev. E, 62, 5313 (2000) |
| [4] | Zhang, Y., Biophys. Chem., 136, 19 (2008) |
| [5] | Block, S. M., J. Cell Biol., 140, 1281 (1998) |
| [6] | Vale, R. D., Cell, 112, 467 (2003) |
| [7] | Reimann, P.; Van den Broeck, C.; Linke, H.; Hänggi, P.; Rubi, J. M.; Pérez-Madrid, A., Phys. Rev. E, 65, 031104 (2002) |
| [8] | Reimann, P.; Van den Broeck, C.; Linke, H.; Hanggi, P.; Rubi, J. M.; Pérez-Madrid, A., Phys. Rev. Lett., 87, 010602 (2001) |
| [9] | Derrida, B., J. Stat. Phys., 31, 433 (1983) |
| [10] | von Gehlen, S.; Evstigneev, M.; Reimann, P., Phys. Rev. E, 77, 031136 (2008) |
| [11] | Evstigneev, M.; Zvyagolskaya, O.; Bleil, S.; Eichhorn, R.; Bechinger, C.; Reimann, P., Phys. Rev. E, 77, 041107 (2008) |
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