Ionization of a model atom by perturbations of the potential

@article{Rokhlenko1999IonizationOA,
  title={Ionization of a model atom by perturbations of the potential},
  author={Alexander Rokhlenko and Joel L. Lebowitz},
  journal={Journal of Mathematical Physics},
  year={1999},
  volume={41},
  pages={3511-3522}
}
We study the time evolution of the wave function of a particle bound by an attractive δ-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 |θ(t)|2, following a pulse of strength r and duration t, behaves as |θ(t)|2−|θ(∞)|2∼t−α, with both θ(∞) and… 

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References

SHOWING 1-10 OF 49 REFERENCES

Exact Results for the Ionization of a Model Quantum System preprint

We prove that a model atom having one bound state will be fully ionized by a time periodic potential of arbitrary strength r and frequency ω. Starting with the system in the bound state, the survival

Multiphoton processes in an intense laser field: Harmonic generation and total ionization rates for atomic hydrogen.

Several formal aspects of Floquet theory, including the convergence of the induced dipole moment, gauge invariance, and the normalization of the wave function are addressed, as well as the influence of resonances on the ionization rates.

Short-time multiphoton detachment in a one-dimensional model with very-short-range potential.

It is shown that the intensity dependence of the cross section of the process is related to different ponderomotive thresholds and for very-low-intensity fields and very short times ``non-energy-conserving'' terms are dominant.

Some results on the quantum dynamics of a particle in a Markovian potential

We consider the quantum dynamics of a particle in a time dependent potentialV(t), assuming it to be a Markovian random function of time. We derive a formula for the density matrix at timet averaged

MULTIPHOTON IONIZATION OF ATOMS

Presents an overview of the current understanding of multiphoton ionization of atoms. It begins with an introductory section to explain the background of the subject. Then the article develops the

On the influence of pulse shapes on ionization probability

We investigate analytical expressions for the upper and lower bounds for the ionization probability through ultra-intense short-pulse laser radiation. We take several different pulse shapes into

Coherence in Spontaneous Radiation Processes

By considering a radiating gas as a single quantum-mechanical system, energy levels corresponding to certain correlations between individual molecules are described. Spontaneous emission of radiation

Survival and Nonescape Probabilities for Resonant and Nonresonant Decay

In this paper we study the time evolution of the decay process for a particle confined initially in a finite region of space, extending our analysis given recently ({ital Phys}. {ital Rev}. {ital

Nonautonomous Hamiltonians

We present a theory of resonances for a class of nonautonomous Hamiltonians to treat the structural instability of spatially localized and time-periodic solutions associated with an unperturbed