Ionization in damped time-harmonic fields

Details Ionization in damped time-harmonic fields Ionization in damped time-harmonic fields

2009-01-06

arxiv.org/abs/0901.0724v1

Physics

Mathematical Physics

Scientific paper

We study the asymptotic behavior of the wave function in a simple one dimensional model of ionization by pulses, in which the time-dependent potential is of the form $V(x,t)=-2\delta(x)(1-e^{-\lambda t} \cos\omega t)$, where $\delta$ is the Dirac distribution. We find the ionization probability in the limit $t\to\infty$ for all $\lambda$ and $\omega$. The long pulse limit is very singular, and, for $\omega=0$, the survival probability is $const \lambda^{1/3}$, much larger than $O(\lambda)$, the one in the abrupt transition counterpart, $V(x,t)=\delta(x)\mathbf{1}_{\{t\ge 1/\lambda\}}$ where $\mathbf{1}$ is the Heaviside function.

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