Hypersensitivity to perturbation in the quantum kicked top

Abstract

For the quantum kicked top we study numerically the distribution of Hilbert-space vectors evolving in the presence of a small random perturbation. For an initial coherent state centered in a chaotic region of the classical dynamics, the evolved perturbed vectors are distributed essentially like random vectors in Hilbert space. In contrast, for an initial coherent state centered near an elliptic (regular) fixed point of the classical dynamics, the evolved perturbed vectors remain close together, explore only few dimensions of Hilbert space, and do not explore them randomly. These results support and extend results of earlier studies, thereby providing additional support for a new characterization of quantum chaos that uses concepts from information theory.