Anomalous diffusion in quantum Brownian motion with colored noise

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 73, Issue 3, 2006, Pages

  Ford, G W ^a,b   O'Connell, R F ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANOMALOUS DIFFUSION; COLORED NOISE; ELECTRON INTERACTING; FLUCTUATION-DISSIPATION THEOREM; QUANTUM BROWNIAN MOTION; RADIATION FIELD;

DIFFUSION; ELECTRONS; QUANTUM THEORY; SPURIOUS SIGNAL NOISE; THERMODYNAMICS; WAVES;

BROWNIAN MOVEMENT;

EID: 33644764774     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.73.032103     Document Type: Article

References (28)

1. J. Klafter and I. M. Sokolov, Phys. World PHWOEW 0953-8585 18 (8), 29 (2005).
2. M. F. de Andrade, Phys. Lett. A PYLAAG 0375-9601 347, 160 (2005).
3. E. Lutz, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.051106 64, 051106 (2001).
4. C. Tsallis and D. J. Bukman, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.R2197 54, R2197 (1996).
5. M. O. Scully, G. Sussmann, and C. Benkert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.60.1014 60, 1014 (1988).
6. M. O. Scully, M. S. Zubairy, and K. Wodkiewicz, Opt. Commun. OPCOB8 0030-4018 65, 440 (1988).
7. C. Benkert, M. O. Scully, A. A. Rangwala, and W. Schleich, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.42.1503 42, 1503 (1990).
8. S. Schaufler, W. P. Schleich, and V. P. Yakovlev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.3162 83, 3162 (1999).
9. H. Grabert, P. Schramm, and G.-L. Ingold, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.58.1285 58, 1285 (1987).
10. H. B. Callen and T. A. Welton, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.83.34 83, 34 (1951).
11. G. W. Ford, J. T. Lewis, and R. F. O'Connell, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(88)90047-4 185, 270 (1988).
12. G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.37.4419 37, 4419 (1988).
13. Tables of Integral Transforms, edited by staff of the Bateman Manuscript Project, Vol. 1 (McGraw-Hill, New York, 1954).
14. G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.55.2273 55, 2273 (1985).
15. G. W. Ford and R. F. O'Connell, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.3112 57, 3112 (1998).
16. G. W. Ford and R. F. O'Connell, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01022833 57, 803 (1989).
17. G. W. Ford and J. T. Lewis, Probability, Statistical Mechanics, and Number Theory, Advances in Mathematics Supplemental Studies, Vol. 9 (Academic Press, Orlando, FL, 1986).
18. G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.032101 64, 032101 (2001).
19. L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1949), p. 58.
20. A. Einstein, Eine neue Bestimmung der Moleküldimensionen (Wyss, Bern, 1905) (Einstein's thesis);
21. A. Einstein, Ann. Phys. ANPYA2 0003-3804 17, 549 (1905);
22. this and the further articles of Einstein appear in Investigations on the Theory of the Brownian Movement (Dover, New York, 1956).
23. R. Brown, Philos. Mag. PHMAA4 0031-8086 4, 161 (1828);
24. R. Brown, Philos. Mag. PHMAA4 0031-8086 6, 161 (1829).
25. M. P. Langevin, C. R. Hebd. Seances Acad. Sci. COREAF 0001-4036 146, 530 (1908)
26. [a translation of this article appears in D. S. Lemons and A. Gythiel, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.18725 65, 1079 (1997)].
27. S. Chandrasekhar, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.15.1 15, 1 (1943).
28. V. Hakim and V. Ambegaokar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.32.423 32, 423 (1985). So far as we know, this paper contains the first derivation of the width of a spreading wave packet, equivalent to our Eq. 5 4, but only for the Ohmic case. Also, we note a misprint in their expression (38) for the width.