Absolute Continuity of the Floquet Spectrum for a Nonlinearly Forced Harmonic Oscillator

TL;DR

This paper proves that the Floquet spectrum of certain time-periodic Schrödinger equations with nonlinear resonant forcing is purely absolutely continuous, advancing understanding of spectral properties in nonlinear quantum systems.

Contribution

It establishes the absolute continuity of the Floquet spectrum for a class of nonlinear, time-periodic Schrödinger equations, a novel result in spectral theory.

Findings

Floquet spectrum is purely absolutely continuous under specified conditions.

Nonlinear resonant forcing does not induce singular spectrum.

Results contribute to spectral analysis of nonlinear quantum systems.

Abstract

We prove that the Floquet spectrum of a class of time-periodic Schroedinger equations under a a mildly nonlinear resonant forcing is purely absolutely continuous.