Phantoms of regularity in the sea of quantum chaos

The concept of the effective quasi-Hamiltonian of a quantum map is proposed. It is shown, using Chirikovʹs standard map as an example, how such a Hamiltonian is constructed in the form of a power expansion near the points of the quantum resonances. In these points, the evolution is connected to continuous gauge transformations from the unitary unimodular group. Within some domain near a resonance of the order q, the evolution turns out to be equivalent to the regular conservative motion along a circle in a (q2−1)-component inhomogeneous “magnetic” field of a particle with q intrinsic degrees of freedom described by the SU(q) group.