HYPERSENSITIVITY TO PERTURBATIONS IN THE QUANTUM BAKERS MAP

We analyze a randomly perturbed quantum version of the baker's transfo rmation, a prototype of an area-conserving chaotic map. By simulating the perturbed evolution, we estimate the information needed to follow a perturbed Hilbert-space vector in time. We find that the Landauer er asure cost associated with this grows very rapidly and becomes larger than the maximum statistical entropy given by the logarithm of the dim ension of Hilbert space. The quantum baker's map displays a hypersensi tivity to perturbations analogous to behavior found in the classical c ase. This hypersensitivity characterizes ''quantum chaos'' in a way th at is relevant to statistical physics.