Quantum Resonances of Kicked Rotor and SU(q) group
Abstract
The quantum kicked rotor (QKR) map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. In some vicinity of a quantum resonance of order
q
, we relate the problem to the {\it regular} motion along a circle in a
(
q
2
−1)
-component inhomogeneous "magnetic" field of a quantum particle with
q
intrinsic degrees of freedom described by the
SU(q)
group. This motion is in parallel with the classical phase oscillations near a non-linear resonance.