Exponential decay and resonances in a driven system

Philippe Briet (1) , Claudio Fernandez (2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 Facultad de Matemáticas [Santiago de Chile]

We study the resonance phenomena for time periodic perturbations of a Hamiltonian $H$ on the Hilbert space $L^2( \mathbb R ^d)$. Here, resonances are characterized in terms of time behavior of the survival probability. Our approach uses the Floquet-Howland formalism combined with the results of L. Cattaneo, J.M. Graf and W. Hunziker on resonances for time independent perturbations.

Keywords: Time dependent perturbation; Schrödinger equation; resonances

Domains: Spectral Theory [math.SP]

Philippe Briet, Claudio Fernandez. Exponential decay and resonances in a driven system. Journal of Mathematical Analysis and Applications, 2012, 396 (02), pp.513-522. ⟨10.1016/j.jmaa.2012.06.040⟩. ⟨hal-00668081v4⟩