Abstract
Quantum relaxation is studied in coupled quantum baker's maps. The classical systems are exactly solvable Kolmogorov systems, for which the exponential decay to equilibrium is known. They model the fundamental processes of transport in classically chaotic phase space. The quantum systems, in the absence of global symmetry, show a marked saturation in the level of transport, as the suppression of diffusion in the quantum kicked rotor, and eigenfunction localization in the position basis. In the presence of a global symmetry we study another model that has classically an identical decay to equilibrium, but-quantally shows resonant transport, no saturation, and large fluctuations around equilibrium. We generalize the quantization to finite multibaker maps. As a byproduct we introduce some simple models of quantal tunneling between classically chaotic regions of phase space.
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References
Y. Elskens and R. Kapral,J. Stat. Phys. 38:1027 (1985).
M. J. Giannoni, A. Voros, and J. Zinn-Justin, eds.,Chaos and Quantum Physics (Elsevier, Amsterdam, 1990).
L. E. Reichl,The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations (Springer-Verlag, New York 1992).
M. C. Gutzwiller,Chaos in Classical and Quantum Mechanics (Springer-Verlag, New York 1990).
F. M. Izrailev,Phys. Rep. 196:299 (1990).
J. H. Hannay and M. V. Berry,Physica D 1:267 (1980).
N. L. Balazs and A. Voros,Ann. Phys. (N.Y.)190:1 (1989).
E. B. Bogomolny,Nonlinearity 5:805 (1992).
R. S. MacKay, J. D. Meiss, and I. C. Percival,Physica D 13:55 (1984).
O. Bohigas, S. Tomsovic, and D. Ullmo, preprint;Phys. Rep., to appear.
I. P. Cornfeld, S. V. Formin, and Ya. G. Sinai,Ergodic Theory (Springer-Verlag, Berlin, 1982).
P. W. O'Connor and S. Tomsovic,Ann. Phys. (N.Y.)207:218 (1991).
P. W. O'Connor, S. Tomsovic, and E. J. Heller,Physica D,55:340 (1992).
A. M. O. De Almeida and M. Saraceno,Ann. Phys. (N. Y.)210:1 (1991).
M. Saraceno,Ann. Phys. (N.Y.)199:37 (1990).
S. W. McDonald and A. N. Kaufman,Phys. Rev. Lett. 42:1189 (1979).
Shmuel Fishman, D. R. Grampel, and R. E. Prange,Phys. Rev. Lett. 49:509 (1982).
E. J. Heller,Phys. Rev. A 35:1360 (1987).
M. J. Davis and E. J. Heller,J. Chem. Phys. 75:246 (1981).
P. Gaspard,J. Stat. Phys. 68:673 (1992).
I. C. Percival, InChaos and Quantum Physics, M. J. Giannoni, A. Voros, and J. Zinn-Justin eds. (Elsevier, Amsterdam, 1990).
E. J. Heller, InChaos and Quantum Physics, M. J. Giannoni, A. Voros, and J. Zinn-Justin, eds. (Elsevier, Amsterdam, 1990).
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Lakshminarayan, A., Balazs, N.L. Relaxation and localization in interacting quantum maps. J Stat Phys 77, 311–344 (1994). https://doi.org/10.1007/BF02186844
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DOI: https://doi.org/10.1007/BF02186844