Topological aspects of quantum chaos.
Quantized classically chaotic maps on a toroidal two-dimensional phase space are studied. A discrete, topological criterion for phase-space localization is presented. To each eigenfunction is associated an integer, analogous to a quantized Hall conductivity, which tests the way the eigenfunction explores the phase space as some boundary conditions are changed. The correspondence between delocalization and chaotic classical dynamics is discussed, as well as the role of degeneracies of the eigenspectrum in the transition from localized to delocalized states. The general results are illustrated with a particular model.
Leboeuf
P.
P
Division de Physique Theorique,(a)) Institut de Physique Nucleaire, 91406 Orsay Cedex, FranceDipartimento di Fisica, Universita di Roma "La Sapienza," Ple A. Moro 2, Rome, ItalyDepartment of Physics, Ben-Gurion University, Beer-Sheva 84105, IsraelDepartment of Physics, B-019, University of California at San Diego, La Jolla, California 92093.
Kurchan
J.
J
Feingold
M.
M
Arovas
D. P.
DP