Treffer: Transition state geometry near higher-rank saddles in phase space
Title:
Transition state geometry near higher-rank saddles in phase space
Authors:
Source:
Nonlinearity (Bristol. Print). 24(2):527-561
Publisher Information:
Bristol: Institute of Physics, 2011.
Publication Year:
2011
Physical Description:
print, 67 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Fonctions de plusieurs variables complexes et espaces analytiques, Several complex variables and analytic spaces, Equations différentielles, Ordinary differential equations, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Champ extérieur, External field, Campo exterior, Champ électrique, Electric field, Campo eléctrico, Espace phase, Phase space, Espacio fase, Etat transition, Transition state, Estado transitorio, Géométrie, Geometry, Geometría, Invariant, Invariante, Ionisation, Ionization, Ionización, Mécanique céleste, Celestial mechanics, Mecánica celeste, Méthode col, Saddle point method, Método punto en puerto, Physique mathématique, Mathematical physics, Física matemática, Point col, Saddle point, Punto silla, Principe invariance, Invariance principle, Principio invarianza, Propriété transport, Transport properties, Propiedad transporte, Rang, Rank, Rango, Réaction chimique, Chemical reaction, Reacción química, Système hamiltonien, Hamiltonian system, Sistema hamiltoniano, Variété invariante, Invariant manifold, Variedad invariante, 32Q45, 34K19, 37D10, 37Jxx, 37N05, Point selle, Surface hyperbolique, Théorie invariant, Variété hyperbolique
Document Type:
Fachzeitschrift
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mechanical Engineering and Department of Mathematics and Statistics, McGill University, Montreal, QC H3A 2K6, Canada
Center for Nonlinear Sciences, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, United States
Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain
Department of Chemistry, West Virginia University, Morgantown, WV 26506-6045, United States
Center for Nonlinear Sciences, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, United States
Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain
Department of Chemistry, West Virginia University, Morgantown, WV 26506-6045, United States
ISSN:
0951-7715
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.23840104
Database:
PASCAL Archive
Weitere Informationen
We present a detailed analysis of invariant phase space structures near higher-rank saddles of Hamiltonian systems. Using the theory of pseudo-hyperbolic invariant surfaces, we show the existence of codimension-one normally hyperbolic invariant manifolds that govern transport near the higher-rank saddle points. Such saddles occur in a number of problems in celestial mechanics, chemical reactions, and atomic physics. As an example, we consider the problem of double ionization of helium in an external electric field, a basis of many modem ionization experiments. In this example, we illustrate our main results on the geometry and transport properties near a rank-two saddle.