Deterministic inhomogeneous ratchet in a periodic potential. (English) Zbl 07908469
Summary: We numerically investigate the deterministic dynamics of a one-dimensional particle in a symmetric periodic potential under the influence of an external periodic force. Additionally, we introduce asymmetry into the system by applying a space-time dependent frictional force. A simple physical example of the theoretical problem studied might be the propagation of a longitudinal sound wave in a symmetric periodic system. This leads to compression and rarefaction in the medium, resulting in particles being subjected to a damping force that periodically fluctuates in both space and time. Our objective is to investigate whether, during this process, net particle transport can be achieved within the considered inhomogeneous deterministic ratchet system and explore the necessary conditions for this to occur. We identify the various regimes of particle motion as manifested by the particle mean velocity as a function of the driving force amplitude. There are primarily three regimes: periodic intrawell, periodic interwell, and chaotic regimes observed. Ratchet effect is observed in both the periodic interwell and chaotic regimes; however, our focus lies on studying particle dynamics within the periodic interwell regime and exploring any relation between the constant ensemble-averaged current in that regime and the frequencies of the frictional force and applied external force. Furthermore, we demonstrate multiple dynamical attractors present under certain circumstances in the system analysed.
MSC:
| 70Fxx | Dynamics of a system of particles, including celestial mechanics |
Keywords:
particle transport; space-time dependent friction coefficient; ratchet current; bifurcation; periodic interwell motionReferences:
| [1] | Feynman, R. P.; Leighton, R. B.; Sands, M., The Feynman Lectures on Physics, vol. I, 1966, Addison-Wesley: Addison-Wesley Reading, Massachusetts, Chapter 46 |
| [2] | Maxwell, J. C., Theory of Heat Ch. 22, 1871, Longmans, Green and Co.: Longmans, Green and Co. London |
| [3] | Maxwell, J. C.; Tait, P. G., (Knott, Cargill Gilston, Life and Scientific Work of Peter Guthrie Tait, 1868, University Press: University Press Cambridge), 213-214 |
| [4] | Leff, H. S.; Rex, A. F., Maxwell’S Demon, 1990, Adam Hilger: Adam Hilger Bristol |
| [5] | Maxwell, J. C.; Tait, P. G., (Harman, P. M., Reproduced in the Scientific Letters and Papers of James Clerk Maxwell, vol. II, 1867, Cambridge Univ. Press: Cambridge Univ. Press Cambridge, UK), 331-332, 1862-1873 |
| [6] | Maxwell, J. C.; Tait, P. G., (Harman, P. M., Reproduced in the Scientific Letters and Papers of James Clerk Maxwell, vol. III, 1875, Cambridge Univ. Press: Cambridge Univ. Press Cambridge, UK), 185-187, 1874-1879 |
| [7] | Smoluchowski, M. V., Phys. Z., 13, 1069, 1912 · JFM 43.1033.04 |
| [8] | Reimann, P.; Hänggi, P., Appl. Phys. A, 75, 169-178, 2002 |
| [9] | Reimann, P., Phys. Rep., 57, 361, 2002 · Zbl 1001.82097 |
| [10] | Astumian, R. D.; Hänggi, P., Phys. Today, 55, 11, 33, 2002 |
| [11] | Hänggi, P.; Marchesoni, F., Rev. Modern Phys., 81, 387, 2009 |
| [12] | Van den Broeck, C.; Kawai, R.; Meurs, P., Phys. Rev. Lett., 93, Article 090601 pp., 2004 |
| [13] | Van den Broeck, C.; Meurs, P.; Kawai, R., New J. Phys., 7, 10, 2005 |
| [14] | Hänggi, P.; Łuczka, J.; Spiechowicz, J., Acta Phys. Pol. B, 51, 1131, 2020 · Zbl 07913317 |
| [15] | Jiao, Y.; Yang, F.; Zeng, C., Eur. Phys. J. Plus, 135, 711, 2020 |
| [16] | Jiao, Y.; Zeng, C.; Luo, Y., Chaos, 33, Article 093140 pp., 2023 |
| [17] | Ajdari, A.; Prost, J., C. R. Acad. Sci. Paris, 315, 4635, 1992 |
| [18] | Magnasco, M. O., Phys. Rev. Lett., 71, 1477, 1993 |
| [19] | Flach, S.; Yevtushenko, O.; Zolotaryuk, Y., Phys. Rev. Lett., 84, 11, 2000 |
| [20] | Astumian, R. D., Science, 276, 917, 1997 |
| [21] | Jülicher, F.; Ajdari, A.; Prost, J., Rev. Modern Phys., 69, 1269, 1997 |
| [22] | Hänggi, P.; Bartussek, R., (Parisi, J.; Müller, S. C.; Zimmermann, W., Nonlinear Physics of Complex Systems. Nonlinear Physics of Complex Systems, Lecture Notes in Physics, vol. 476, 1996, Springer: Springer Berlin), 294-308 |
| [23] | Mateos, J. L., Phys. D, 168-169, 205-219, 2002 · Zbl 0998.82032 |
| [24] | Luchsinger, R. H., Phys. Rev. E, 62, 1, 2000 |
| [25] | Saikia, S.; Mahato, M. C., Phys. A, 389, 4052, 2010 |
| [26] | Reenbohn, W. L.; Pohlong, S. S.; Mahato, Mangal C., Phys. Rev. E, 85, Article 031144 pp., 2012 |
| [27] | Reenbohn, W. L.; Mahato, Mangal C., Phys. Rev. E, 91, Article 052151 pp., 2015 |
| [28] | Kharkongor, D.; Reenbohn, W. L.; Mahato, Mangal C., Phys. Rev. E, 94, Article 022148 pp., 2016 |
| [29] | Saikia, S., Phys. A, 468, 219-227, 2017 · Zbl 1400.82255 |
| [30] | Kharkongor, D.; Mahato, Mangal C., Eur. J. Phys., 39, Article 065002 pp., 2018 · Zbl 07670124 |
| [31] | Kharkongor, D., J. Stat. Mech., Article 033209 pp., 2018 |
| [32] | Spiechowicz, J.; Marchenko, I. G.; Hänggi, P.; Łuczka, J., Entropy, 25, 42, 2023 |
| [33] | Sawkmie, I. S.; Mahato, Mangal C., Commun. Nonlinear Sci. Numer. Simul., 78, Article 104859 pp., 2019 · Zbl 1475.70021 |
| [34] | Sawkmie, I. S.; Mahato, Mangal C., Phys. Educ., 1, Article 1950015 pp., 2019 |
| [35] | Sawkmie, I. S.; Mahato, M. C., Int. J. Bifurc. Chaos, 30, 15, Article 2030046 pp., 2020 · Zbl 1477.70042 |
| [36] | Kharkongor, B.; Pohlong, S. S.; Mahato, Mangal C., Phys. A, 562, Article 125341 pp., 2021 · Zbl 07542633 |
| [37] | Martínez, P. J.; Chacón, R., Nonlinear Dynam., 111, 12973-12982, 2023 |
| [38] | Borromeo, M.; Marchesoni, F., Phys. Lett. A, 249, 199-203, 1998 |
| [39] | Kharkongor, B.; Kharmawlong, P. M.; Pohlong, S. S.; Mahato, Mangal C., Phys. D, 457, Article 133982 pp., 2024 · Zbl 1535.34048 |
| [40] | Bartussek, R.; Hänggi, P.; Kissner, J. G., Europhys. Lett., 28, 7, 459, 1994 |
| [41] | Hondou, T.; Sawada, Y., Phys. Rev. Lett., 75, 3269, 1995 |
| [42] | Jung, P.; Kissner, J. G.; Hänggi, P., Phys. Rev. Lett., 76, 3436, 1996 |
| [43] | Barbi, M.; Salerno, M., Phys. Rev. E, 62, 2, 2000 |
| [44] | Mateos, J. L., Phys. Rev. Lett., 84, 258, 2000 |
| [45] | Borromeo, M.; Constantini, G.; Marchesoni, F., Phys. Rev. E, 65, Article 041110 pp., 2002 |
| [46] | Marchesoni, F.; Savelev, S.; Nori, F., Phys. Rev. E, 73, Article 021102 pp., 2006 |
| [47] | Carusela, M. F.; Fendrik, A. J.; Romanelli, L., Phys. A, 388, 4017, 2009 |
| [48] | Mateos, J. L., Acta. Phys. Polon. B, 32, 307, 2001 |
| [49] | Barbi, M.; Salerno, M., Phys. Rev. E, 63, Article 066212 pp., 2001 |
| [50] | Mateos, J. L., Commun. Nonlinear Sci. Numer. Simul., 8, 253, 2003 · Zbl 1065.70016 |
| [51] | Family, F.; Larrondo, H. A.; Zarlenga, D. G.; Arizmendi, C. M., J. Phys.: Condens. Matter., 17, 3719, 2005 |
| [52] | Vincent, U. E.; Njah, A. N.; Laoye, J. A., Phys. D, 231, 130-136, 2007 · Zbl 1127.34034 |
| [53] | Luo, Y.; Zeng, C.; Ai, Bao-Quan, Phys. Rev. E, 102, Article 042114 pp., 2020 |
| [54] | Luo, Y.; Zeng, C.; Huang, T.; Ai, Bao-Quan, Phys. Rev. E, 106, Article 034208 pp., 2022 |
| [55] | Büttiker, M., Z. Phys. B, 68, 161, 1987 |
| [56] | Sullivan, D. B.; Zimmerman, J. E., Am. J. Phys., 39, 1504, 1971 |
| [57] | Rochlin, G. I.; Hansma, P. K., Am. J. Phys., 41, 878, 1973 |
| [58] | Falco, C. M., Am. J. Phys., 44, 8, 1976 |
| [59] | Desloge, E. A., Am. J. Phys., 62, 601, 1994 |
| [60] | Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T., Numerical Recipes, 1987, Cambridge University Press: Cambridge University Press Cambridge, UK |
| [61] | Mannella, R., (Freund, J. A.; Pöschel, T., A Gentle Introduction to the Integration of Stochastic Differential Equations in Stochastic Processes in Physics, Chemistry and Biology. A Gentle Introduction to the Integration of Stochastic Differential Equations in Stochastic Processes in Physics, Chemistry and Biology, Lecture Notes in Physics, vol. 557, 2000, Springer: Springer Berlin), 353 |
| [62] | Kenfack, A.; Sweetnam, S. M.; Pattanayak, A. K., Phys. Rev. E, 75, Article 056215 pp., 2007 |
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