2004/08/01 by Ovidiu Costin, O. Costin, Rodica D. Costin +3
Mathematics · Physics and Astronomy · #Delocalized electron #Disjoint sets #Floquet theory #Laplace transform #Mathematical analysis #Mathematical physics #Mathematics #Parametric statistics #Perturbation (astronomy) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Spectral Theory in Mathematical Physics #Wave function #math-ph #math.MP #msc:35P99 #msc:46N50 #msc:81S99
paper · pdf · doi:10.1023/b:joss.0000037244.42209.f7
published as J. Stat. Phys.1--4 283-310 (2004)
openalex publication_date 2004/08/01 · arxiv created 2006/08/13 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the transition to the continuum of an initially bound quantum particle in \RRd, d=1,2,3, subjected, for t≥ 0, to a time periodic forcing of arbitrary magnitude. The analysis is carried out for compactly supported potentials, satisfying certain auxiliary conditions. It provides complete analytic information on the time Laplace transform of the wave function. From this, comprehensive time asymptotic properties (Borel summable transseries) follow. We obtain in particular a criterion for whether the wave function gets fully delocalized (complete ionization). This criterion shows that complete ionization is generic and provides a convenient test for particular cases. When satisfied it implies absence of discrete spectrum and resonances of the associated Floquet operator. As an illustration we show that the parametric harmonic perturbation of a potential chosen to be any nonzero multiple of the characteristic function of a measurable compact set has this property.