On the Spectrum of the Resonant Quantum Kicked Rotor
Italo Guarneri
TL;DR
This paper proves that the quasi-energy spectrum bands of the Quantum Kicked Rotor are never flat at any primitive resonance, providing perturbative estimates of bandwidths at small kick strength for prime order resonances.
Contribution
It establishes that no flat bands occur at primitive resonances and offers perturbative estimates for bandwidths, highlighting the impact of spectral degeneracies.
Findings
No flat bands at any primitive resonance.
Bandwidths scale differently due to degeneracies.
Perturbative estimates for small kick strength.
Abstract
It is proven that none of the bands in the quasi-energy spectrum of the Quantum Kicked Rotor is flat at any primitive resonance of any order. Perturbative estimates of bandwidths at small kick strength are established for the case of primitive resonances of prime order. Different bands scale with different powers of the kick strength, due to degeneracies in the spectrum of the free rotor.
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