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
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.