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The quantum kicked rotor 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 (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 nonlinear resonance.

physical review letters

Quantum Resonances of the Kicked Rotor and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>SU</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">q</mml:mi><mml:mo>)</mml:mo></mml:math>Group

Quantum Resonances of the Kicked Rotor and theSU(q)Group