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Ionization of a Model Atom by Perturbations of the Potential
Mathematical Physics · Submitted 19 May 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Thus the survival probability of bound state $|\theta(t)|^2$, following a pulse of strength $r$ and duration $t$, behaves as $|\theta(t)|^2 -|\theta(\infty)|^2 \sim t^{-\alpha}$, with both $\theta(\infty)$ and $\alpha$ depending on $r$.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
We study the time evolution of the wave function of a particle bound by an attractive $\delta$-function potential when it is subjected to time dependent variations of the binding strength (parametric excitation). The simplicity of this model permits certain nonperturbative calculations to be carried out analytically both in one and three dimensions. Thus the survival probability of bound state $|\theta(t)|^2$, following a pulse of strength $r$ and duration $t$, behaves as $|\theta(t)|^2 -|\theta(\infty)|^2 \sim t^{-\alpha}$, with both $\theta(\infty)$ and $\alpha$ depending on $r$. On the other hand a sequence of strong short pulses produces an exponential decay over an intermediate time scale.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the time evolution of the wave function of a particle bound by an attractive $\delta$-function potential when it is subjected to time dependent variations of the binding strength (parametric excitation). | contribution 0.97 | 0.90 | 0.06 | asserted 0.94 |
| s1 | The simplicity of this model permits certain nonperturbative calculations to be carried out analytically both in one and three dimensions. | method 0.93 | 0.58 | 0.04 | asserted 0.76 |
| s2 | Thus the survival probability of bound state $|\theta(t)|^2$, following a pulse of strength $r$ and duration $t$, behaves as $|\theta(t)|^2 -|\theta(\infty)|^2 \sim t^{-\alpha}$, with both $\theta(\infty)$ and $\alpha$ depending on $r$. | result 1.00 | 0.88 | 0.39 | asserted 1.00 |
| s3 | On the other hand a sequence of strong short pulses produces an exponential decay over an intermediate time scale. | result 1.00 | 0.85 | 0.22 | asserted 1.00 |
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The paper
Original abstract
We study the time evolution of the wave function of a particle bound by an attractive $\delta$-function potential when it is subjected to time dependent variations of the binding strength (parametric excitation). The simplicity of this model permits certain nonperturbative calculations to be carried out analytically both in one and three dimensions. Thus the survival probability of bound state $|\theta(t)|^2$, following a pulse of strength $r$ and duration $t$, behaves as $|\theta(t)|^2 -|\theta(\infty)|^2 \sim t^{-\alpha}$, with both $\theta(\infty)$ and $\alpha$ depending on $r$. On the other hand a sequence of strong short pulses produces an exponential decay over an intermediate time scale.
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