RECORD
Kepler map
chao-dyn · Submitted 12 Apr 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We reveal that transition from adiabatic to chaotic ionization takes place when the ratio of the field frequency to the electron Kepler frequency approximately equals 0.1.
The compiled record
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.
Open the compiled record
The abstract, sentence by sentence
We present a consecutive derivation of mapping equations of motion for the one-dimensional classical hydrogenic atom in a monochromatic field of any frequency. We analyze this map in the case of high and low relative frequency of the field and transition from regular to chaotic behavior. We show that the map at aphelion is suitable for investigation of transition to chaotic behavior also in the low frequency field and even for adiabatic ionization when the strength of the external field is comparable with the Coulomb field. Moreover, the approximate analytical criterion (taking into account the electron's energy increase by the influence of the field) yields a threshold field strength quite close to the numerical results. We reveal that transition from adiabatic to chaotic ionization takes place when the ratio of the field frequency to the electron Kepler frequency approximately equals 0.1. For the dynamics and ionization in a very low frequency field the Kepler map can be converted to a differential equation and solved analytically. The threshold field of the adiabatic ionization obtained from the map is only 1.5% lower than the exact field strength of static field ionization.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a consecutive derivation of mapping equations of motion for the one-dimensional classical hydrogenic atom in a monochromatic field of any frequency. | contribution 0.95 | 0.96 | 0.08 | asserted 0.99 |
| s1 | We analyze this map in the case of high and low relative frequency of the field and transition from regular to chaotic behavior. | contribution 0.86 | 0.93 | 0.09 | asserted 0.92 |
| s2 | We show that the map at aphelion is suitable for investigation of transition to chaotic behavior also in the low frequency field and even for adiabatic ionization when the strength of the external field is comparable with the Coulomb field. | result 0.85 | 0.92 | 0.27 | asserted 0.99 |
| s3 | Moreover, the approximate analytical criterion (taking into account the electron's energy increase by the influence of the field) yields a threshold field strength quite close to the numerical results. | result 0.96 | 0.93 | 0.11 | asserted 0.98 |
| s4 | We reveal that transition from adiabatic to chaotic ionization takes place when the ratio of the field frequency to the electron Kepler frequency approximately equals 0.1. | result 1.00 | 0.93 | 0.35 | asserted 0.99 |
| s5 | For the dynamics and ionization in a very low frequency field the Kepler map can be converted to a differential equation and solved analytically. | method 0.54 | 0.88 | 0.08 | asserted 0.82 |
| s6 | The threshold field of the adiabatic ionization obtained from the map is only 1.5% lower than the exact field strength of static field ionization. | result 1.00 | 0.92 | 0.16 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We present a consecutive derivation of mapping equations of motion for the one-dimensional classical hydrogenic atom in a monochromatic field of any frequency. We analyze this map in the case of high and low relative frequency of the field and transition from regular to chaotic behavior. We show that the map at aphelion is suitable for investigation of transition to chaotic behavior also in the low frequency field and even for adiabatic ionization when the strength of the external field is comparable with the Coulomb field. Moreover, the approximate analytical criterion (taking into account the electron's energy increase by the influence of the field) yields a threshold field strength quite close to the numerical results. We reveal that transition from adiabatic to chaotic ionization takes place when the ratio of the field frequency to the electron Kepler frequency approximately equals 0.1. For the dynamics and ionization in a very low frequency field the Kepler map can be converted to a differential equation and solved analytically. The threshold field of the adiabatic ionization obtained from the map is only 1.5% lower than the exact field strength of static field ionization.
Human review
How the literature uses it
Papers whose main result relates to this one's
States the same result 1 paper
-
We show that transition from adiabatic to chaotic ionization mechanism takes place when the field frequency to the electron's Kepler frequency ration approximately equals 0.1.
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.