Abstract
Quantum Brownian motion of a rod-like particle is investigated in the frame work of system plus reservoir model. The quantum mechanical and classical limit for both translational and rotational motions are discussed. Correlation functions, fluctuation-dissipation relations and mean squared values of translational and rotational motions are obtained.
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Einstein, A.: Ann. Phys. 17, 549 (1905)
Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (2012)
Langevin, P.: Comptes Rendues 146, 530 (1908)
Uhlenbeck, G. E., Ornstein, L. S.: Phys. Rev. 36(5), 823 (1930)
Smoluchowski, M.: Ann. Phys. 21, 756 (1906)
Wiener, N.: Extrapolation, interpolation, and smoothing of stationary time series. Cambridge (1949)
Kolmogorov, A.: Foundations of the Theory of Probability. New York (1956)
Doob, J. L.: (1942)
Levy, P.: Compos. Math. 7, 283 (1940)
Nykypanchuk, D., Strey, H. H., Hoagland, D. A.: Science 297, 987 (2002)
Perrin, J.: Nature 86, 105 (1911)
Harko, T., Mocanu, G.: Eur. Phys. J. C 76(3), 1 (2016)
Sandoval, M., Velasco, R. M., Jiménez-Aquino, J. I.: Phys. A 442, 321 (2016)
Cobanera, E., Kristel, P., Smith, C. M.: arXiv preprint arXiv:1602.00694
Saffman, P.G., Delbrück, M.: Proc. Natl. Acad. Sci. 72(8), 3111 (1975)
Frey, E., Kroy, K.: arXiv preprint cond-mat/0502602
Jou, I. A., Melnikov, D. V., Gracheva, M. E.: Nanotechnology 27(20), 205201 (2016)
Ghosh, S. K., Chattaraj, P. K.: Concepts and Methods in Modern Theoretical Chemistry: Statistical Mechanics. Taylor and Francis Group, New York (2013)
Waldron, J. T., Kalmykov, Y. P., Coffey, W. T.: Phys. Rev. E 49(5), 3976 (1994)
Meng, X., Zhang, J.W., Guo, H.: Phys. A 452, 281 (2016)
Hubbard, P. S.: Phys. Rev. A 15(1), 329 (1977)
Gardiner, C. W.: Handbook of Stochastic Methods. Springer, Berlin (1985)
Hubbard, P. S.: Phys. Rev. A 8(3), 1429 (1973)
Patriarca, M., Sodano, P.: arXiv preprint arXiv:1605.04698
Weiss, U.: Quantum Dissipative Systems. World scientific, Singapore (1999)
Lahiri, R., Sain, A.: Pramana 62(5), 1015 (2004)
Caldeira, A. O., Leggett, A. J.: Phys. A 121(3), 587 (1983)
Grabert, H., Schramm, P., Ingold, G. L.: Phys. Rep. 168(3), 115 (1988)
Hu, B. L., Paz, J. P., Zhang, Y.: Phys. Rev. D 45(8), 2843 (1992)
Hu, B. L., Paz, J. P., Zhang, Y.: Phys. Rev. D 47(4), 1576 (1993)
Fleming, C. H., Roura, A., Hu, B. L.: Ann. Phys. 326(5), 1207 (2011)
Calzetta, E., Roura, A., Verdaguer, E.: Int. J. Theor. Phys. 40(12), 2317 (2001)
Ford, G. W., Lewis, J. T., O’Connell, R. F.: Phys. Rev. A 37(11), 4419 (1988)
Oppenheim, I., Romero-Rochin, V.: Phys. A 147(1), 184 (1987)
Thakur, V. K., Kessler, M. R.: Liquid Crystalline Polymers. Springer, Switzerland (2016)
Riseman, J., Kirkwood, J. G.: J. Chem. Phys. 18(4), 512 (1950)
Semenov, A. N.: Faraday Trans. 2: Mol. Chem. Phys. 82(3), 317 (1986)
De la Torre, J. G., Huertas, M. L., Carrasco, B.: J. Magn. Reson. 147(1), 138 (2000)
Steinhoff, H.J., Hubbell, W. L.: Biophys. J. 71(4), 2201 (1996)
Hakim, V., Ambegaokar, V.: Phys. Rev. A 32(1), 423 (1985)
Caldeira, A. O., Leggett, A. J.: Phys. A 121, 587 (1983)
Dekker, H.: Phys. Rep. 80(1), 1 (1981)
Yurke, B.: Am. J. Phys. 54(12), 1133 (1986)
Dekker, H.: Phys. Rev. A 31(2), 1067 (1985)
Gompper, G., Schick, M. (eds.): Soft Matter: Vol. 2, Complex Colloidal Suspensions. Wiley-VCH, New York (2006)
Philbin, T. G., Anders, J.: J. Phys. A Math. Theor. 49(21), 215303 (2016)
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Nasr, Z., Kheirandish, F. System Plus Reservoir Approach to Quantum Brownian Motion of a Rod-Like Particle. Int J Theor Phys 56, 2140–2150 (2017). https://doi.org/10.1007/s10773-017-3356-0
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DOI: https://doi.org/10.1007/s10773-017-3356-0