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Ionization in a 1-Dimensional Dipole Model

O. Costin·J. L. Lebowitz·C. Stucchio
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Abstract

We study the evolution of a one dimensional model atom with $δ$-function binding potential, subjected to a dipole radiation field $E(t) x$ with $E(t)$ a $2π/ω$-periodic real-valued function. Starting with $ψ(x,t=0)$ an initially localized state and $E(t)$ a trigonometric polynomial, complete ionization occurs; the probability of finding the electron in any fixed region goes to zero. For $ψ(x,0)$ compactly supported and general periodic fields, we construct a resonance expansion. Each resonance is given explicitly as a Gamow vector, and is $2π/ω$ periodic in time and behaves like the exponentially growing Green's function near $x=\pm \infty$. The remainder is given by an asymptotic power series in $t^{-1/2}$ with coefficients varying with $x$.

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O. Costin, J. L. Lebowitz, C. Stucchio. 2007-06-04. Ionization in a 1-Dimensional Dipole Model. https://arxiv.org/abs/math-ph/0609069

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