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IONIZATION IN A 1-DIMENSIONAL DIPOLE MODEL

Department of Mathematics, The Ohio State University, 100 Math Tower, Columbus, OH 43210-1174, USA

Department of Mathematics and Physics, Rutgers, The State University of New Jersey, Hill Center, Busch Campus, New Brunswick, New Jersey 08901, USA

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, and

C. STUCCHIO

Courant Institute, New York University, New York, NY 10012-1185, USA

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https://doi.org/10.1142/S0129055X08003419Cited by:8 (Source: Crossref)

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. We prove that when E(t) is a trigonometric polynomial, complete ionization occurs, i.e. the probability of finding the electron in any fixed region goes to zero as t → ∞.

For ψ(x, t = 0) compactly supported and general periodic fields, we decompose ψ(x, t) into uniquely defined resonance terms and a remainder. Each resonance is 2π/ω periodic in time and behaves like the exponentially growing Green's function near x = ±∞. The remainder is given by an asymptotic power series in t^-1/2 with coefficients varying with x.

Keywords:

AMSC: 47A53, 35P25, 81V45, 35B34, 35B10, 35Q40

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