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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, .

Lattice theory. --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical

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This handbook presents electronic structure data and tabulations of Slater-Koster parameters for the whole periodic table. This second edition presents data sets for all elements up to Z = 112, Copernicium, whereas the first edition contained only 53 elements. In this new edition, results are given for the equation of state of the elements together with the parameters of a Birch fit, so that the reader can regenerate the results and derive additional information, such as Pressure-Volume relations and variation of Bulk Modulus with Pressure. For each element, in addition to the equation of state, the energy bands, densities of states, and a set of tight-binding parameters is provided. For a majority of elements, the tight-binding parameters are presented for both a two- and three-center approximation. For the hcp structure, new three-center tight-binding results are given. Other new material in this edition include: energy bands and densities of states of all rare-earth metals, a discussion of the McMillan-Gaspari-Gyorffy theories, and a tabulation of the electron-ion interaction matrix elements. The evaluation of the Stoner criterion for ferromagnetism is examined and results are tabulated. This edition also contains two new appendices discussing the effects of spin-orbit interaction and a modified version of Harrison's tight-binding theory for metals which puts the theory on a quantitative basis.

Physics. --- Solid State Physics. --- Spectroscopy and Microscopy. --- Materials Science, general. --- Condensed Matter Physics. --- Crystallography. --- Theoretical, Mathematical and Computational Physics. --- Materials. --- Physique --- Cristallographie --- Matériaux --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Energy-band theory of solids --- Band theory of solids --- Condensed matter. --- Solid state physics. --- Spectroscopy. --- Microscopy. --- Materials science. --- Conduction band --- Crystallography, Mathematical --- Electrons --- Exciton theory --- Molecules --- Quantum theory --- Solids --- Wave mechanics --- Crystallography and Scattering Methods. --- Leptology --- Physical sciences --- Mineralogy --- Engineering --- Engineering materials --- Industrial materials --- Engineering design --- Manufacturing processes --- Materials --- Mathematical physics. --- Physical mathematics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Material science --- Analysis, Microscopic --- Light microscopy --- Micrographic analysis --- Microscope and microscopy --- Microscopic analysis --- Optical microscopy --- Optics --- Analysis, Spectrum --- Spectra --- Spectrochemical analysis --- Spectrochemistry --- Spectrometry --- Spectroscopy --- Chemistry, Analytic --- Interferometry --- Radiation --- Wave-motion, Theory of --- Absorption spectra --- Light --- Spectroscope --- Mathematics --- Qualitative --- Analytical chemistry