O. Costin, J. L. Lebowitz, C. Stucchio and S. Tanveer
Exact Results for Ionization of Model Atomic Systems
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ABSTRACT. We present rigorous results for quantum systems with both bound and continuum states subjected to an arbitrary strength time-periodic field. We prove that the wave function takes the form $\psi(x,t) = \sum_{j} \sum_{k=0}^{N_{j}-1} t^{k} e^{-i \sigma_{j} t}c_{j} \phi_{j,k}(x,t) + \psi_{d}(x,t)$, with $\phi_{j,k}(x,t)$ a set of time-periodic resonant states with quasi-energies $\sigma_{j}=E_{j}-i\Gamma_{j}/2$, with $E_{j}$ the Stark-shifted energy and $\Gamma_{j}$ the ionization rate, and $N_{j}$ the multiplicity of each resonance. $\psi_{d}(x,t)$ is the dispersive part of the the solution, and is given by a power series in $t^{-1/2}$. Generally, $\Gamma_{j} > 0$ for each $j$ leading to ionization of the atom, but we also give examples where $\Gamma_{j}=0$ and implying the existence of a time-periodic Floquet bound state. The quantity $\sigma_{j}=E_{j}-i\Gamma_{j}/2$ has a convergent perturbation expansion for small field strengths.