| Titre : |
Bornes inférieures pour les systèmes à petit nombre de corps |
| Type de document : |
texte imprimé |
| Auteurs : |
Kheir-Eddine Boudjema ; Univ. de Constantine, Éditeur scientifique ; S.R. Zouzou, Directeur de thèse |
| Année de publication : |
2007 |
| Importance : |
178 p. |
| Note générale : |
01 Disponible à la salle de recherche 02 Disponibles au magazin de la B.U.C. 01 CD |
| Langues : |
Français (fre) |
| Catégories : |
Français - Anglais
Physique
|
| Tags : |
Optimisation Méthode variationnelle Oscillateur harmonique Fonction d'onde d'essai Hamiltonien Gaissienne corrélée Borne supérieure Borne inférieure Contrainte dynamique universelle Saturabilité |
| Index. décimale : |
530 Physique |
| Résumé : |
This thesis deals with few body systems, although most of the results we obtain apply
equally well to N-body systems with arbitrary N. Most of this thesis is devoted to the
study of a lower bound for the ground state energy of N-body systems, governed by nonrelativistic kinematics and translationally invariant two-body interactions. The originality
of this lower bound relies in the fact that it results from an optimization process over a
number of parameters. This lower bound is correspondingly called optimized lower bound.
It proves that the values of the parameters corresponding to the optimized lower bound
satisfy a certain number of relations called universal dynamical constraints, dynamical
because these relations are of dynamical nature since resulting from a dynamical principle,
i.e., the variational principle, and universal because these relations are independent of the
particular form of the potential. A large part of this thesis has been devoted to a derivation
of these universal dynamical constraints which in addition to their theoretical interest are
extremely important on practical grounds, leading to a spectacular simpliÖcation of the
optimization process. This derivation has been made completely and in the more general
case for three, four and Öve body problems and partially for problems with more than Öve
particles. A very interesting property of the optimized lower bound is its saturability in
the particular case of harmonic interactions. This property of saturability has never been
taken in default, and we are now convinced of its general character. Morever, we have
proved analytically this property of saturability for special mass conÖgurations but for
arbitrary N. Partially because of this we have been lead to derive compact expressions for
the N-body harmonic oscillator exact energies in the case of special mass conÖgurations. In
addition, our optimized lower bound proves to be absolutely superior or better than naive
and impoved lower bounds. Furthermore, our optimized lower bound is of so high quality
that it may even be taken as an excellent approximation to the exact N-body ground
state energy, in competition with very sophisticated variational calculations, which give
an upper bound for the N-body ground state energy. |
| Diplôme : |
Doctorat en sciences |
| En ligne : |
../theses/physique/BOU4981.pdf |
| Format de la ressource électronique : |
pdf |
| Permalink : |
index.php?lvl=notice_display&id=3510 |
Bornes inférieures pour les systèmes à petit nombre de corps [texte imprimé] / Kheir-Eddine Boudjema ; Univ. de Constantine, Éditeur scientifique ; S.R. Zouzou, Directeur de thèse . - 2007 . - 178 p. 01 Disponible à la salle de recherche 02 Disponibles au magazin de la B.U.C. 01 CD Langues : Français ( fre)
| Catégories : |
Français - Anglais
Physique
|
| Tags : |
Optimisation Méthode variationnelle Oscillateur harmonique Fonction d'onde d'essai Hamiltonien Gaissienne corrélée Borne supérieure Borne inférieure Contrainte dynamique universelle Saturabilité |
| Index. décimale : |
530 Physique |
| Résumé : |
This thesis deals with few body systems, although most of the results we obtain apply
equally well to N-body systems with arbitrary N. Most of this thesis is devoted to the
study of a lower bound for the ground state energy of N-body systems, governed by nonrelativistic kinematics and translationally invariant two-body interactions. The originality
of this lower bound relies in the fact that it results from an optimization process over a
number of parameters. This lower bound is correspondingly called optimized lower bound.
It proves that the values of the parameters corresponding to the optimized lower bound
satisfy a certain number of relations called universal dynamical constraints, dynamical
because these relations are of dynamical nature since resulting from a dynamical principle,
i.e., the variational principle, and universal because these relations are independent of the
particular form of the potential. A large part of this thesis has been devoted to a derivation
of these universal dynamical constraints which in addition to their theoretical interest are
extremely important on practical grounds, leading to a spectacular simpliÖcation of the
optimization process. This derivation has been made completely and in the more general
case for three, four and Öve body problems and partially for problems with more than Öve
particles. A very interesting property of the optimized lower bound is its saturability in
the particular case of harmonic interactions. This property of saturability has never been
taken in default, and we are now convinced of its general character. Morever, we have
proved analytically this property of saturability for special mass conÖgurations but for
arbitrary N. Partially because of this we have been lead to derive compact expressions for
the N-body harmonic oscillator exact energies in the case of special mass conÖgurations. In
addition, our optimized lower bound proves to be absolutely superior or better than naive
and impoved lower bounds. Furthermore, our optimized lower bound is of so high quality
that it may even be taken as an excellent approximation to the exact N-body ground
state energy, in competition with very sophisticated variational calculations, which give
an upper bound for the N-body ground state energy. |
| Diplôme : |
Doctorat en sciences |
| En ligne : |
../theses/physique/BOU4981.pdf |
| Format de la ressource électronique : |
pdf |
| Permalink : |
index.php?lvl=notice_display&id=3510 |
|
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