dorsal/arxiv
View SchemaStabilization not for certain and the usefulness of bounds
| Authors | C. Figueira de Morisson Faria, A. Fring, R. Schrader |
|---|---|
| Categories | |
| ArXiv ID | physics/9912032 |
| URL | https://arxiv.org/abs/physics/9912032 |
| Journal | Proc. 8-th Int. Conf. on Multiphothon Processes, ed. L.F. DiMauro et.al. (1999) 150 |
Abstract
Stabilization is still a somewhat controversial issue concerning its very existence and also the precise conditions for its occurrence. The key quantity to settle these questions is the ionization probability, for which hitherto no computational method exists which is entirely agreed upon. It is therefore very useful to provide various consistency criteria which have to be satisfied by this quantity, whose discussion is the main objective of this contribution. We show how the scaling behaviour of the space leads to a symmetry in the ionization probability, which can be exploited in the mentioned sense. Furthermore, we discuss how upper and lower bounds may be used for the same purpose. Rather than concentrating on particular analytical expressions we obtained elsewhere for these bounds, we focus in our discussion on the general principles of this method. We illustrate the precise working of this procedure, its advantages, shortcomings and range of applicability. We show that besides constraining possible values for the ionization probability these bounds, like the scaling behaviour, also lead to definite statements concerning the physical outcome. The pulse shape properties which have to be satitisfied for the existence of asymptotical stabilization is the vanishing of the total classical momentum transfer and the total classical displacement and not smoothly switched on and off pulses. Alternatively we support our results by general considerations in the Gordon-Volkov perturbation theory and explicit studies of various pulse shapes and potentials including in particular the Coulomb- and the delta potential.
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"abstract": "Stabilization is still a somewhat controversial issue concerning its very\nexistence and also the precise conditions for its occurrence. The key quantity\nto settle these questions is the ionization probability, for which hitherto no\ncomputational method exists which is entirely agreed upon. It is therefore very\nuseful to provide various consistency criteria which have to be satisfied by\nthis quantity, whose discussion is the main objective of this contribution. We\nshow how the scaling behaviour of the space leads to a symmetry in the\nionization probability, which can be exploited in the mentioned sense.\nFurthermore, we discuss how upper and lower bounds may be used for the same\npurpose. Rather than concentrating on particular analytical expressions we\nobtained elsewhere for these bounds, we focus in our discussion on the general\nprinciples of this method. We illustrate the precise working of this procedure,\nits advantages, shortcomings and range of applicability. We show that besides\nconstraining possible values for the ionization probability these bounds, like\nthe scaling behaviour, also lead to definite statements concerning the physical\noutcome. The pulse shape properties which have to be satitisfied for the\nexistence of asymptotical stabilization is the vanishing of the total classical\nmomentum transfer and the total classical displacement and not smoothly\nswitched on and off pulses. Alternatively we support our results by general\nconsiderations in the Gordon-Volkov perturbation theory and explicit studies of\nvarious pulse shapes and potentials including in particular the Coulomb- and\nthe delta potential.",
"arxiv_id": "physics/9912032",
"authors": [
"C. Figueira de Morisson Faria",
"A. Fring",
"R. Schrader"
],
"categories": [
"physics.atom-ph"
],
"journal_ref": "Proc. 8-th Int. Conf. on Multiphothon Processes, ed. L.F. DiMauro\n et.al. (1999) 150",
"title": "Stabilization not for certain and the usefulness of bounds",
"url": "https://arxiv.org/abs/physics/9912032"
},
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