Border between regular and chaotic quantum dynamics.
We identify a border between regular and chaotic quantum dynamics. The border is characterized by a power-law decrease in the overlap between a state evolved under chaotic dynamics and the same state evolved under a slightly perturbed dynamics. For example, the overlap decay for the quantum kicked top is well fitted with [1+(q-1)(t/tau)2](1/(1-q)) (with the nonextensive entropic index q and tau depending on perturbation strength) in the region preceding the emergence of quantum interference effects. This region corresponds to the edge of chaos for the classical map from which the quantum chaotic dynamics is derived.
Weinstein
Yaakov S
YS
Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Lloyd
Seth
S
Tsallis
Constantino
C