EDP Sciences
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laboutique.edpsciences.fr/833/9782759819522
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EDP Sciences
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Current Natural Sciences
<TitleType>01</TitleType>
<TitleText>Introduction to Louis Michel's lattice geometry through group action</TitleText>
1
A01
B.
Zhilinskii
2
A01
Michel
Leduc
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A01
Michel
Le Bellac
<p>Michel Le Bellac est professeur émérite à l’Université de Nice-Sophia Antipolis. Ses travaux portent sur la physique théorique des particules élémentaires et la théorie quantique des champs à température finie.<br />Il est l’auteur de plusieurs manuels de physique à un niveau avancé et de deux livres dans la présente collection, « Le monde quantique » et « Les relativités ». Il est aussi co-auteur, toujours dans cette collection, de « Le temps : mesurable, réversible, insaisissable ».</p>
NED
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eng
262
23
Physique Générale
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02
<p style="text-align: justify;">Group action analysis developed and applied mainly by Louis Michel to the study of N-dimensional periodic lattices is the central subject of the book. Di erent basic mathematical tools currently used for the description of lattice geometry are introduced and illustrated through applications to crystal structures in two- and three-dimensional space, to abstract multi-dimensional lattices and to lattices associated with integrable dynamical systems. Starting from general Delone sets the authors turn to di erent symmetry and topological classi- cations including explicit construction of orbifolds for two- and three-dimensional point and space groups.</p>
<p align="LEFT">Voronoï and Delone cells together with positive quadratic forms and lattice description by root systems are introduced to demonstrate alternative approaches to lattice geometry study. Zonotopes and zonohedral families of 2-, 3-, 4-, 5-dimensional lattices are explicitly visualized using graph theory approach. Along with crystallographic applications, qualitative features of lattices of quantum states appearing for quantum problems associated with classical Hamiltonian integrable dynamical systems are shortly discussed.</p>
<p align="LEFT">The presentation of the material is presented through a number of concrete examples with an extensive use of graphical visualization. The book is aimed at graduated and post-graduate students and young researchers in theoretical physics, dynamical systems, applied mathematics, solid state physics, crystallography, molecular physics, theoretical chemistry, ...</p>
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Group action analysis developed and applied mainly by Louis Michel to the study of N-dimensional periodic lattices is the central subject of the book. Di erent basic mathematical tools currently used for the description of lattice geometry are introduced and illustrated through applications to crystal structures in two- and three-dimensional space, to abstract multi-dimensional lattices and to lattices associated with integrable dynamical systems. Starting from general Delone sets the authors turn to di erent symmetry and topological classi- cations including explicit construction of orbifolds for two- and three-dimensional point and space groups. Voronoï and Delone cells together with positive quadratic forms and lattice description by root systems are introduced to demonstrate alternative approaches to lattice geometry study. Zonotopes and zonohedral families of 2-, 3-, 4-, 5-dimensional lattices are explicitly visualized using graph theory approach. Along with crystallographic applications, qualitative features of lattices of quantum states appearing for quantum problems associated with classical Hamiltonian integrable dynamical systems are shortly discussed. The presentation of the material is presented through a number of concrete examples with an extensive use of graphical visualization. The book is aimed at graduated and post-graduate students and young researchers in theoretical physics, dynamical systems, applied mathematics, solid state physics, crystallography, molecular physics, theoretical chemistry, ...
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https://laboutique.edpsciences.fr/produit/833/9782759819522/Introduction%20to%20Louis%20Michels%20lattice%20geometry%20through%20group%20action
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EDP Sciences
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20160308
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EDP Sciences
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