Perturbation of an eigenvalue from a dense point spectrum: a general Floquet Hamiltonian
| dc.creator | Duclos, P. | |
| dc.creator | Stovicek, P. | |
| dc.creator | Vittot, M. | |
| dc.date | 1997-12-01 | |
| dc.date.accessioned | 2026-07-07T10:15:54Z | |
| dc.date.available | 2026-07-07T10:15:54Z | |
| dc.description | We consider a perturbed Floquet Hamiltonian $-i\partial_t + H + βV(ωt)$ in the Hilbert space $L^2([0,T],E,dt)$. Here $H$ is a self-adjoint operator in $E$ with a discrete spectrum obeying a growing gap condition, $V(t)$ is a symmetric bounded operator in $E$ depending on $t$ $2π$-periodically, $ω= 2π/T$ is a frequency and $β$ is a coupling constant. The spectrum $Spec(-i\partial_t + H)$ of the unperturbed part is pure point and dense in $R$ for almost every $ω$. This fact excludes application of the regular perturbation theory. Nevertheless we show, for almost all $ω$ and provided $V(t)$ is sufficiently smooth, that the perturbation theory still makes sense, however, with two modifications. First, the coupling constant is restricted to a set $I$ which need not be an interval but 0 is still a point of density of $I$. Second, the Rayleigh-Schrodinger series are asymptotic to the perturbed eigen-value and the perturbed eigen-vector. | |
| dc.description | AmsTex, 45 pages | |
| dc.identifier | https://arxiv.org/abs/physics/9712006 | |
| dc.identifier | http://arxiv.org/abs/physics/9712006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173330 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Functional Analysis | |
| dc.subject | Chaotic Dynamics | |
| dc.subject | Quantum Physics | |
| dc.title | Perturbation of an eigenvalue from a dense point spectrum: a general Floquet Hamiltonian | |
| dc.type | text |