Abstract
We study the Hamiltonian of a two-level system interacting with a one-mode radiation field by means of the Wigner method and without using the rotating-wave approximation. We show that a phenomenon of collapses and revival, reminiscent of that exhibited by the Jaynes-Cummings model, takes place in the high-coupling limit. This process appears as irreversible or virtually reversible, according to whether the semiclassical regime is chaotic or not. Thus, we find a new mechanism for dissipation in the quantum domain.
Similar content being viewed by others
References
T. Y. Li and J. A. Yorke,Ann. Math. Mon. 82:985 (1975).
B. J. West,An Essay on the Importance of Being Nonlinear (Springer-Verlag, Berlin, 1985).
J. R. Buchler and H. Eichron, eds.,Chaotic Phenomena in Astrophysics, Ann. N. Y. Acad. Sci. 497 (1987).
H. Bai-Lin, ed.,Directions in Chaos (World Scientific, Singapore, 1987).
R. H. Enns, B. L. Jones, R. M. Muira, and S. S. Rangnekar, eds.,Nonlinear Phenomena in Physics and Biology (Plenum Press, New York, 1981).
R. L. Devaney,An Introduction to Chaotic Dynamical Systems, 2nd ed. (Addison-Wesley, New York, 1989).
J. Guckenheimer and P. Holmes,Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
A. J. Lichtenberg and M. A. Lieberman,Regular and Stochastic Motion (Springer-Verlag, New York, 1983).
E. N. Lorenz,J. Atmos. Sci. 20:130 (1963).
B. J. West,Fractal Physiology and Chaos in Medicine (World Scientific, Singapore, 1990).
R. M. May,Nature 261:459 (1976).
T. Hogg and B. A. Huberman,Phys. Rev. Lett. 48:711 (1982); S. Fishman, D. R. Grempel, and R. E. Prange,Phys. Rev. Lett. 49:509 (1982); G. Casati, B. V. Chirikov, and D. L. Shepelyansky,Phys. Rev. Lett. 53:2525 (1984); P. M. Koch, L. Moorman, B. E. Sauer, and E. J. Galvey, inClassical Dynamics in Atomic and Molecular Processes (World Scientific, Singapore, 1989).
M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner,Phys. Rep. 106:122 (1984).
R. Roncaglia, R. Mannella, D. Vitali, and P. Grigolini, unpublished.
L. Bonci, R. Roncaglia, B. J. West, and P. Grigolini,Phys. Rev. Lett. 67:2593 (1991).
N. B. Nosozhmy, J. J. Sánchez-Mondragón, and J. H. Eberly,Phys. Rev. A 23:236 (1981).
R. R. Puri and G. S. Agerwal,Phys. Rev. A 33:3610 (1986).
S. M. Barnett and P. L. Knight,Phys. Rev. A 33:2444 (1986).
L. Bonci, P. Grigolini, and D. Vitali,Phys. Rev. A 42:4452 (1990).
J. Gea-Banacloche,Phys. Rev. Lett. 65:3385 (1990).
H. Weyl,Z. Phys. 46:1 (1927).
E. T. Jaynes and F. W. Cummings,Proc. IEEE 51:89 (1963).
R. Graham and M. Höhnerbach,Z. Phys.-Cond. Matter 57:233 (1984).
P. I. Belorov, G. M. Zaslavsky, and G. Th. Tartakovsky,Sov. Phys. JETP 44:945 (1976).
P. M. Milonni, J. R. Ackerhalt, and H. W. Galbraith,Phys. Rev. Lett. 50:966 (1983).
L. Allen and J. H. Eberly,Optical Resonance and Two-Level Atoms, Chapter 1 (Wiley-Interscience, New York, 1975).
A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastarro,Physica 16D:285 (1985).
G. Benettin, L. Galgani, and J. M. Strelcyn,Phys. Rev. A 14:2338 (1976).
M. Berry,J. Phys. A 10:2083 (1977).
A. Vorhos, inStochastic Behavior in Classical and Quantum Hamiltonian Systems, G. Casti and J. Ford, eds. (Springer, New York, 1979).
A. J. Lettett, S. Chakravortz, A. T. Dorsey, M. P. A. Fisher, A. Gorg, and W. Zwerger,Rev. Mod. Phys. 59:1 (1987).
D. Vitali and P. Grigolini,Phys. Rev. A 42:4452 (1990).
R. Kubo,J. Math. Phys. 4:174 (1963).
F. W. Cummings,Phys. Rev. A 140:1051 (1965).
K. Lindenberg and B. J. West,The Nonequilibrium Statistical Mechanics of Open and Closed Systems (VCH Publishers, New York, 1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Roncaglia, R., Bonci, L., Grigolini, P. et al. Chaos and quantum irreversibility. J Stat Phys 68, 321–343 (1992). https://doi.org/10.1007/BF01048848
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01048848