Mean Dynamical Entropy of Quantum Maps on the Sphere Diverges in the Semiclassical Limit

Wojciech Słomczyński, Karol Życzkowski
1998 Physical Review Letters  
We show that the mean dynamical entropy of a quantum map on the sphere is positive and tends logarithmically to infinity in the semiclassical limit. A link between chaotic dynamics of classical systems and the random matrix-like properties of spectra of the corresponding quantum analogues is demonstrated.
doi:10.1103/physrevlett.80.1880 fatcat:j3otjxuunvdifbx2cgdcfmu4ra