| ATOMIC AND MOLECULAR PHYSICS |
|
|
|
|
Evolution of Quantum Phase Space Distribution: a Trajectory-Density Approach |
| ZHANG Xue-Feng, ZHENG Yu-Jun |
| School of Physics, Shandong University, Jinan 250100 |
|
| Cite this article: |
|
ZHANG Xue-Feng, ZHENG Yu-Jun 2009 Chin. Phys. Lett. 26 023404 |
|
|
|
|
Abstract The trajectory-density method of a quantum system is developed by using local Koopman and Frobenius-Perron operators. We propose a new scheme of approximation from two sets of trajectory-density mixed equations. By examining the local generation and termination of trajectories, we show how they can be adopted to the propagation of negative values of the Wigner function even if it starts off positive everywhere.
|
| Keywords:
34.10.+x
|
|
|
Received: 30 October 2008
Published: 20 January 2009
|
|
| PACS: |
34.10.+x
|
(General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.))
|
|
|
|
|
|
[1] Wigner E P 1932 Phys. Rev. 40 749
[2] Millery M et al. 1984 Phys. Rep. 106 121
[3] Li Q S, Wei G M and L\"{u L Q 2004 Phys. Rev. A 70 022105
[4] Heller E J 1976 J. Chem. Phys. 65 1289
[5] Heller E J 1977 J. Chem. Phys. 67 3339
[6] Lee H W 1995 Phys. Rep. 259 147
[7] Rasavy M 1996 Phys. Lett. A 212 119
[8] Lee H W and Scully M Q 1982 J. Chem. Phys. 774604
[9] Lee H W and M. O. Scully M Q 1983 Found. Phys. 13 61
[10] Lopreore C L and Wyatt R E 1999 Phys. Rev. Lett. 82 5190
[11] Goldfarb Y, Degani I and Tannor D J 2006 J. Chem.Phys. 125 231103
[12] Burghardt I and Cedebaum L S 2001 J. Chem. Phys. 115 10303
[13] Donoso A and Martens C C 2001 Phys. Rev. Lett. 87 223202
[14] Donoso A Zheng Y and Martens C C 2003 J. Chem.Phys. 119 5010
[15] Pazy A 1983 Semigroups of Linear Operators andApplications to Partial Differential Equations (New York: Springer)
[16] Koopman B O 1931 Proc. Nat. Acad. Sci. 17 315
[17] Lasota A and Machey M 1994 Chaos, Fractals, andNoise: Stochastic Aspects of Dynamics 2nd edn (New York: Springer)
[18] Wang A, Zheng Y, Martens C C and Ren W 2008 Phys.Chem. Chem. Phys. DOI:10.1039/ B811509E
[19] Arnold V I 1992 Ordinary Differential Equations 3rdedn (Berlin: Springer) |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
