Hypersensitivity to Perturbations in the Quantum Baker's Map

Details Hypersensitivity to Perturbations in the Quantum Baker's Map Hypersensitivity to Perturbations in the Quantum Baker's Map

1993-03-06

arxiv.org/abs/chao-dyn/9303002v1

Phys. Rev. Lett. 71, 525 (1993)

Nonlinear Sciences

Chaotic Dynamics

8 pages, LATEX, 3 Postscript figures appended as uuencoded file

Scientific paper

10.1103/PhysRevLett.71.525

We analyze a randomly perturbed quantum version of the baker's transformation, a prototype of an area-conserving chaotic map. By numerically simulating the perturbed evolution, we estimate the information needed to follow a perturbed Hilbert-space vector in time. We find that the Landauer erasure cost associated with this information grows very rapidly and becomes much larger than the maximum statistical entropy given by the logarithm of the dimension of Hilbert space. The quantum baker's map thus displays a hypersensitivity to perturbations that is analogous to behavior found earlier in the classical case. This hypersensitivity characterizes ``quantum chaos'' in a way that is directly relevant to statistical physics.

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