# Ionization in damped time-harmonic fields - Mathematical Physics

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Abstract: We study the asymptotic behavior of the wave function in a simple onedimensional model of ionization by pulses, in which the time-dependentpotential is of the form $Vx,t=-2\deltax1-e^{-\lambda t} \cos\omega t$,where $\delta$ is the Dirac distribution. We find the ionization probability inthe limit $t\to\infty$ for all $\lambda$ and $\omega$. The long pulse limit isvery singular, and, for $\omega=0$, the survival probability is $const\lambda^{1-3}$, much larger than $O\lambda$, the one in the abrupt transitioncounterpart, $Vx,t=\deltax\mathbf{1} {\{t\ge 1-\lambda\}}$ where$\mathbf{1}$ is the Heaviside function.

Author: ** O. Costin, M. Huang, Z. Qiu**

Source: https://arxiv.org/