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• W2032965093 abstract "Double kicked rotors (DKRs) appear to be the simplest nonintegrable Hamiltonian systems featuring classical translational symmetry in phase space (i.e., in angular momentum) for an emph{infinite} set of values (the rational ones) of a parameter $eta$. The experimental realization of quantum DKRs by atom-optics methods motivates the study of the double kicked particle (DKP). The latter reduces, at any fixed value of the conserved quasimomentum $betahbar$, to a generalized DKR, the textquotedblleft $beta $-DKRtextquotedblright . We determine general quantum properties of $beta $-DKRs and DKPs for arbitrary rational $eta $. The quasienergy problem of $beta $-DKRs is shown to be equivalent to the energy eigenvalue problem of a finite strip of coupled lattice chains. Exact connections are then obtained between quasienergy spectra of $beta $-DKRs for all $beta $ in a generically infinite set. The general conditions of quantum resonance for $beta $-DKRs are shown to be the simultaneous rationality of $eta $, $beta$, and a scaled Planck constant $hbar _{mathrm{S}}$. For rational $hbar _{mathrm{S}}$ and generic values of $beta $, the quasienergy spectrum is found to have a staggered-ladder structure. Other spectral structures, resembling Hofstadter butterflies, are also found. Finally, we show the existence of particular DKP wave-packets whose quantum dynamics is emph{free}, i.e., the evolution frequencies of expectation values in these wave-packets are independent of the nonintegrability. All the results for rational $hbar _{mathrm{S}}$ exhibit unique number-theoretical features involving $eta $, $hbar _{mathrm{S}}$, and $beta $." @default.
• W2032965093 created "2016-06-24" @default.
• W2032965093 creator A5057284185 @default.
• W2032965093 date "2015-01-20" @default.
• W2032965093 modified "2023-10-18" @default.
• W2032965093 title "Quantum properties of double kicked systems with classical translational invariance in momentum" @default.
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• W2032965093 doi "https://doi.org/10.1103/physreve.91.012914" @default.
• W2032965093 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/25679689" @default.
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