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 regular motion along a circle in a (q2-1)-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.
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