Stochastic approach to time-dependent quantum tunneling

Russian Journal of Mathematical Physics

Volumn 4, Issue 3, 1996, Pages 275-286

  Chebotarev, Alexander M ^a   Quezada Batalla, R ^b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b DEPARTAMENTO DE QUÍMICA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030336107     PISSN: 10619208     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. Chebotarev, A. M., 'On a stochastic representation of solutions for the Schrödinger equation', Mathematical Notes vol. 24 no. 5 (1978), 873-877.
2. Maslov, V. P. and Chebotarev, A. M., 'Processes de sauts et leurs applications dans la mécanique quantique', Lecture Notes in Phys. vol. 106 (1979), 58-72.
3. Bertrand, J., Gaveau, B., and Rideau, G., 'Poisson processes and quantum field theory', Lecture Notes in Math. vol. 1109 (1985), 74-80.
4. Combe, Ph. et al., 'Generalized Poisson processes in quantum mechanics and field theory', Phys. Rep. vol. 77 (1981), 221-233.
5. Blanchard, Ph., Combe, Ph., Zeng, W., 'Mathematical and physical aspects of stochastic mechanics', Lecture Notes in Phys. vol. 281 (1987).
6. Combe, Ph. et al., 'Quantum dynamical time evolution as stochastic flows on phase space', Physica A vol. 124 (1984), 561-574.
7. Pereyra, P. and Quezada, R., 'Probabilistic representation formulae for the time evolution of quantum systems', JMP vol. 34 (1993), 59-68.
8. Reed, V. C. and Burnett, K., 'Ionization of atoms in intense laser pulses using the Kramers-Hennenberger transformation', Physical Rev. vol. 42 no. 3 (1990), 3152-3155.
9. Kan, S. C. and Yariv, A., 'Lifetime of a quasi-bound state in the quantum well in a double-barrier structure with a localized imaginary potential', J. Appl. Phys. vol. 67 no. 4 (1990), 1957-1961.
10. Tang, X., Rudolph, H., Lambropoulos, P., 'Nonperturbative approach to atomic multiphoton processes under intense short laser pulses', Phys. Rev. Lett. vol. 65 no. 26 (1990), 3269-3272.
11. Deveneaud, B. et al., 'Subpicosecond luminescence study of tunneling and relaxation in coupled quantum wells', Phys. Rev. B vol. 42 no. 11 (1990), 7021-7031.
12. Manthe, U. and Köppel, H., 'New method for calculating wave packet dynamics: strongly coupled surfaces and the adiabatic basis', J. Chem. Phys. vol. 93 no. 1, 345-356.
13. Chebotarev, A. M., 'Approximately complete sets of the generalized Feynman measure', Dokl. Akad. nauk SSSR vol. 298 no. 2 (1988), 52-57.
14. Chebotarev, A. M. and Sobolevski, A. V., 'Monte-Carlo regularisation of Feynman path integral in the momentum representation', COSMEX' 89 International Conference on Stochastic in Experimental Sci. Wroclaw (1989), 13-14.
15. Chebotarev, A. M., Konstantinov, A. A., Maslov, V. P., 'Probabilistic representation of solutions of the Cauchy problem for Schrödinger, Pauli, and Dirac equations', Russian Math. Surv. vol. 45 no. 6 (1990), 3-24.
16. Chebotarev, A. M., 'Sufficient conditions for the regularity of jump Markov process', Theor. Prob. & Appl. vol. 33 no. 1 (1988), 22-35.
17. Kato, T. (1976), Perturbation Theory for Linear Operators, Springer, Berlin.