Trajectory approach to dissipative quantum phase space dynamics: Application to barrier scattering

Journal of Chemical Physics

Volumn 120, Issue 9, 2004, Pages 4089-4097

  Hughes, Keith H ^a,b   Wyatt, Robert E ^a  

^a The University of Texas at Austin   (United States)

^b BANGOR UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BARRIER SCATTERING; DISSIPATIVE SYSTEMS; PHASE SPACE DYNAMICS; WAVE PACKETS;

ALGORITHMS; BROWNIAN MOVEMENT; EQUATIONS OF MOTION; FOURIER TRANSFORMS; HYDRODYNAMICS; NUMERICAL ANALYSIS; POLYNOMIALS; PROBABILITY DISTRIBUTIONS; TRAJECTORIES;

QUANTUM THEORY;

EID: 1842476688     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1643897     Document Type: Article

References (44)

1. E. Wigner, Physica (Utrecht) 7, 749 (1940).
2. H. W. Lee, Phys. Rep. 259, 147 (1995).
3. M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984).
4. A. G. Redfield, Adv. Magn. Reson. 1, 1 (1965).
5. A. O. Caldeira and A. J. Legget, Physica A 121, 587 (1983).
6. G. Lindblad, Commun. Math. Phys. 121, 119 (1976).
7. L. Diosi, Physica A 199, 517 (1993).
8. C. L. Lopreore and R. E. Wyatt, Phys. Rev. Lett. 82, 5190 (1999).
9. V. E. Madelung, Z. Phys. 40, 322 (1926).
10. L. de Broglie, An Introduction to the Study of Wave Mechanics (Dutton, New York, 1930).
11. D. Bohm, Phys. Rev. 85, 166 (1952).
12. D. Bohm, Phys. Rev. 85, 180 (1952).
13. A Lagrangian frame is one that evolves with the equation of motion for the system, i.e., it traces the trajectory of the system.
14. R. E. Wyatt and K. Na, Phys. Rev. E 65, 016702 (2002).
15. K. Na and R. E. Wyatt, Phys. Scr. 20, l (2003).
16. K. Na and R. E. Wyatt, Phys. Rev. A 306, 97 (2002).
17. I. Burghardt and L. S. Cederbaum, J. Chem. Phys. 115, 10303 (2001).
18. I. Burghardt and L. S. Cederbaum, J. Chem. Phys. 115, 10312 (2001).
19. I. Burghardt and K. B. Moller, J. Chem. Phys. 117, 7409 (2002).
20. J. B. Maddox and E. R. Bittner, J. Chem. Phys. 115, 6309 (2001).
21. J. B. Maddox and E. R. Bittner, Phys. Rev. E 65, 026143 (2002).
22. C. J. Trahan, K. H. Hughes, and R. E. Wyatt, J. Chem. Phys. 118, 9911 (2003).
23. E. R. Bittner, J. Chem. Phys. 118, 9911 (2003).
24. C. J. Trahan and R. E. Wyatt, J. Chem. Phys. 119, 7017 (2003).
25. C. J. Trahan and R. E. Wyatt (unpublished).
26. A. Donoso, Y. Zheng, and C. C. Martens, J. Chem. Phys. 119, 5010 (2003).
27. H. A. Kramers, Phys. Rev. 40, 284 (1932).
28. L. E. Ballentine, Quantum Mechanics: A Modern Development (World Scientific, Singapore, 1998), Chap. 15.
29. W. A. Lin and L. E. Ballentine, Phys. Rev. Lett. 65, 2927 (1990).
30. J. Y. Shin and H. W. Lee, Phys. Rev. E 50, 902 (1994).
31. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1993).
32. D. Cohen, C. C. Marston, and D. J. Tannor, J. Chem. Phys. 107, 5236 (1997).
33. R. P. Feynnman and F. L. Vernon, Ann. Phys. 24, 118 (1963).
34. T. Liszka, Int. J. Numer. Methods Eng. 20, 1599 (1984).
35. T. Liszka, C. A. M. Duarte, and W. W. Tworzydlo, Comput. Methods Appl. Mech. Eng. 139, 263 (1996).
36. R. E. Wyatt, J. Chem. Phys. 111, 4406 (1999).
37. L. B. Lucy, Astrophys. J. 82, 1013 (1977).
38. R. A. Gingold and J. J. Monaghan, Mon. Not. R. Astron. Soc. 181, 375 (1977).
39. D. A. Fulk and D. W. Quinn, J. Comp. Physiol. 126, 165 (1996).
40. S. Garashchuck and V. A. Rassolov, Chem. Phys. Lett. 364, 562 (2002).
41. E. R. Bittner and R. E. Wyatt, Comput. Sci. Eng. 5, 22 (2003).
42. n.
43. qq in Figs. 4(b) and 4(d).
44. W. G. Unruh and W. H. Zurek, Phys. Rev. D 40, 1071 (1989).