Chaotic electronic scattering with He+

Yuan, Jian‐Min; Gu, Yan

doi:10.1063/1.165961

Cited by 9 publications

(4 citation statements)

References 37 publications

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“…As the first investigations indicate [74], the tori around stable periodic orbits can be successfully used for carrying out a semiclassical quantization. In [75] Yuan and Gu investigated the scattering of an electron on a Helium ion.…”

Section: Hydrodynamical Processes It Has Long Been Knownmentioning

confidence: 99%

New developments in classical chaotic scattering

Seoane

Sanjuán

2012

Rep. Prog. Phys.

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Classical chaotic scattering is a topic of fundamental interest in nonlinear physics due to the numerous existing applications in fields such as celestial mechanics, atomic and nuclear physics and fluid mechanics, among others. Many new advances in chaotic scattering have been achieved in the last few decades. This work provides a current overview of the field, where our attention has been mainly focused on the most important contributions related to the theoretical framework of chaotic scattering, the fractal dimension, the basins boundaries and new applications, among others. Numerical techniques and algorithms, as well as analytical tools used for its analysis, are also included. We also show some of the experimental setups that have been implemented to study diverse manifestations of chaotic scattering. Furthermore, new theoretical aspects such as the study of this phenomenon in time-dependent systems, different transitions and bifurcations to chaotic scattering and a classification of boundaries in different types according to symbolic dynamics are also shown. Finally, some recent progress on chaotic scattering in higher dimensions is also described.

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Section: Hydrodynamical Processes It Has Long Been Knownmentioning

confidence: 99%

New developments in classical chaotic scattering

Seoane

Sanjuán

2012

Rep. Prog. Phys.

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“…A large amount of work has been done on potential scattering (i.e. scattering of an elementary particle on fixed potential centers) [2][3][4][5], but also the scattering among at least three interacting bodies has received great attention (see the work of Petit and Hénon on the scattering between a planet and two satellites [6], or the system helium nucleus plus two electrons [7]). A monographic issue about this subject has been published in the journal CHAOS [8].…”

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confidence: 99%

Chaos in coplanar classical collisions with particles interacting throughr−2forces

Sattin

Salasnich

1999

Phys. Rev. E

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The scattering among three particles interacting through 1/r 2 forces, with opposite charges and widely different masses, is studied in a coplanar geometry. The present work shows that at low impact velocities the output of the collision presents typical characteristics of chaos. The details of the process are investigated. ͓S1063-651X͑99͒07701-6͔PACS number͑s͒: 05.45. Ϫa, 34.70.ϩe Starting from the works of Gaspard and Rice ͓1͔, chaotic scattering was found to be ubiquitous. A large amount of work has been done on potential scattering ͑i.e., scattering of an elementary particle on fixed potential centers͒ ͓2-5͔, but also the scattering among at least three interacting bodies has received great attention ͑see the work of Petit and Hénon on the scattering between a planet and two satellites ͓6͔ or the system helium nucleus plus two electrons ͓7͔͒. A monographic issue about this subject has been published in ͓8͔.In all these studies the projectile and a target preserve their internal structure during the collision, but one can analyze also reactive collisions. Kovács and Wiesenfeld ͓9͔ studied, in a collinear geometry, the scattering between an atom and a diatomic molecule: AϩBC↔ABC↔ABϩC. More recently, we studied the chaotic behavior in the reaction between a hydrogen atom ͑proton plus electron͒ and a projectile proton interacting through Coulomb forces ͓10͔. We analyzed the full three-dimensional problem at very low impact energies. We found that the transition from regular to chaotic scattering appears when impact velocity v p is reduced to a value below about 1/10 of the classical electron velocity v e .In this paper we present another investigation on the same subject: We think that it is worth consideration since collisions with rearrangement between electrically charged particles are one current topic in atomic physics, from both the theoretical and the experimental points of view ͓11͔. The phase space of a system of three particles moving in three dimensions is too large to be easily handled; limiting to two dimensions will allow us to do a more detailed and accurate study. We will address the following topics. ͑a͒ Do features of chaotic scattering appear in two-dimensional collisions? ͑b͒ If so, do they appear in the form of a sharp order-chaos transition or as a smooth transition? ͑c͒ Is it possible to detect some traces of irregular behavior also in the heavy particles motion, instead of only when looking at the lightest one? ͑d͒ Finally, an investigation of the dynamics of the electron during the scattering is done. It gives insight into how the discontinuities on the output function appear.The final state of the projectile may be defined through a set of parameters ͕A f ͖ ͑e.g., the angle of deflection and final velocity͒, which are functions of the input quantities ͕A i ͖ ͑e.g., the impact parameter and impact velocity͒. When the set of values ͕A f ͖ depends sensitively by ͕A i ͖, i.e., a finite variation of ͕A f ͖ is caused by an infinitesimal variation of ͕A i ͖, the system is chaotic.Usually, on...

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“…Another example is the occurrence of the chaotic scattering due to collisions [2]. We know that there are many processes related to the collision phenomena in the real world, such as chemical reactions [3], celestial mechanics [4], charged particles in an electromagnetic field [5], processes in hydrodynamics [6], scattering in atomic physics [7], and transportation problems in mesoscopic physics [8], etc.…”

Section: Introductionmentioning

confidence: 99%

Classical and quantum chaotic behaviors of two colliding harmonic oscillators

Zheng

Zhang

1996

Physics Letters A

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We have systematically studied both classical and quantum chaotic behaviors of two colliding harmonic oscillators. The classical case falls in Kolmogorov-Arnold-Moser class. It is shown that there exists an energy threshold, above which the system becomes nonintegrable. For some values of the initial energy near the threshold, we have found that the ratio of frequencies of the two oscillators affects the Poincaré sections significantly. The largest Lyapunov character exponent depends linearly on the ratio of frequencies of the two oscillators away from the energy threshold in some chaotic regions, which shows that the chaotic behaviors of the system are mainly determined by the ratio.In the quantum case, for certain parameters, the distribution of the energy level spacings also varies with the ratio of frequencies of the two oscillators.The relation between the energy spectra and the ratio of frequencies of the two oscillators, the interaction constant, and the semi-classical quantization constant, is also investigated respectively.

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Chaotic electronic scattering with He+

Cited by 9 publications

References 37 publications

New developments in classical chaotic scattering

New developments in classical chaotic scattering

Chaos in coplanar classical collisions with particles interacting throughr−2forces

Classical and quantum chaotic behaviors of two colliding harmonic oscillators

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