Hypersensitivity to perturbation in the quantum kicked top
Physical Review E, 1994•APS
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 a few dimensions of Hilbert space …
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 a few dimensions of Hilbert space …
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 a few dimensions of Hilbert space, and do not explore them randomly. These results support and extend the results of earlier studies, thereby providing additional support for a characterization of quantum chaos that uses concepts from information theory.
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