Collection(s) : Current natural sciences
Paru le 04/12/2015 | Relié V-262 pages
Doctorat
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. Different 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 different symmetry and topological classifications including explicit construction of orbifolds for two- and three-dimensional point and space groups.
Voronoï and Delone celles 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 visual zation. 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, ...
Book series edited by Michèle Leduc and Michel Le Bellac.
Louis Michel (1923-1999) became in 1962 the first permanent professor in physics at l'Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France a world center of interaction between mathematicians and physicists. In 1984, Louis Michel received Wigner medal for his contribution to the formulation and use of the symmetry principles.
Boris Zhilinskii worked as researcher at Chemistry department of Moscow State University (Lomonosov) during 1970-1992. Since 1993 he is professor at Université du Littoral Côte d'Opale, Dunkerque, France. During 1991-1999 he collaborated with Louis Michel on application of group-theoretical and topological methods in molecular physics.
