Absolute continuity of the Floquet spectrum for a nonlinearly forced harmonic oscillator

Authors
Graffi, S Yajima, K
Citation
S. Graffi et K. Yajima, Absolute continuity of the Floquet spectrum for a nonlinearly forced harmonic oscillator, COMM MATH P, 215(2), 2000, pp. 245-250
Citations number
10
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN journal
00103616 → ACNP
Volume
215
Issue
2
Year of publication
2000
Pages
245 - 250
Database
ISI
SICI code
0010-3616(200012)215:2<245:ACOTFS>2.0.ZU;2-M
Abstract
We prove that the Floquet spectrum of the time periodic Schrodinger equatio n i partial derivativeu/partial derivativet = -1/2 Deltau + 1/2x(2)u + 2 ep silon (sint)x(1)u + muV(t, x)u, corresponding to a mildly nonlinear resonan t forcing, is purely absolutely continuous for mu suitably small.