No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Topological aspects of quantum chaos
1.A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1984).
2.P. Leboeuf, J. Kurchan, M. Feingold, and D. P. Arovas, Phys. Rev. Lett. 65, 3076 (1990).
3.F. D. M. Haldane and E. H. Rezayi, Phys. Rev. B 31, 2529 (1985).
4.P. Leboeuf and A. Voros, J. Phys. A: Math. Gen. 23, 1765 (1990).
5.E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge U. P., Cambridge, 1965), Chap. 21.
6.See M. V. Berry, N. L. Balazs, M. Tabor, and A. Voros, Ann. Phys. (NY) 122, 26 (1979) for a general discussion.
7.B. Simon, Phys. Rev. Lett. 51, 2167 (1983).
8.M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
9.A. Shapere and F. Wilczek, Geometric Phases in Physics (World Scientific, Singapore, 1989).
10.J. von Neumann and E. Wigner, Phys. Z. 30, 467 (1929).
11.D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
12.M. Kohmoto, Ann. Phys. (NY) 160, 343 (1985).
13.D. P. Arovas, R. N. Bhatt, F. D. M. Haldane, P. B. Littlewood, and R. Rammal, Phys. Rev. Lett. 60, 619 (1988).
14.J. Kurchan, P. Leboeuf, and M. Saraceno, Phys. Rev. A 40, 6800 (1989).
15.Multiple-well type potentials where exponentially small spectral degeneracies occur, are examples ofintegrable systems where all the quantum states have a nonzero Chern number; this phenomenon is due to delicate resonances in which the particle tunnels from one well to the other as the boundary conditions are changed, and Eq. (18) is not valid in this case (see Ref. 11 for a more detailed discussion). An arbitrary perturbation, as for example the kicking studied in Sec. IV, will destroy the phenomenon.
16.See A. J. Stone, Proc. R. Soc. London Ser. A 351, 141 (1976) for a more detailed explanation of this construction.
17.For even N there are two states associated with the classical separatrix which become degenerate at the Chern number of this pair of bands remains well denned and is
Article metrics loading...
Full text loading...
Most read this month
Most cited this month