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Quantum Resonances of Kicked Rotor and SU(q) group

V. V. Sokolov·O. V. Zhirov·D. Alonso·G. Casati
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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.

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V. V. Sokolov, O. V. Zhirov, D. Alonso, G. Casati. 1999-07-26. Quantum Resonances of Kicked Rotor and SU(q) group. https://doi.org/10.1103/physrevlett.84.3566

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