The aim of this successful book is to describe and analyse peculiarities of classical and quantum dynamics of a crystal as a spatially periodic structure. In the second revised and updated edition, the author focuses on low-dimensional models of crystals and on superlattices. Both traditional questions like the spectrum of vibrations, the idea of phonon gas, dislocations etc. and new aspects like the theory of quantum crystals, solitons in 1D crystals, dislocation theory of melting of 2D crystals etc. are discussed. The author gives an explanation of a set of phenomena which entered into solid state physics during the last decades. It is shown that the crystal properties are sensitive to the dimension of the crystal and its defect structure, and depend slightly on whether the periodic structure consists of atoms, or electrical dipoles, or magnetic moments (spins). Considerable attention is devoted to the dislocation mechanisms as a basis of the theory of plasticity and numerous technological applications of crystalline materials.

Thema dieses erfolgreichen Buches sind die klassische Mechanik und die Quantenmechanik von Kristallen. Sowohl die idealen Kristalle als auch nichtideale Kristallgitter mit Störstellen werden behandelt. Besondere Aufmerksamkeit gilt der Dynamik anisotroper und niedrigdimensionaler Kristalle sowie Problemen der Versetzungsdynamik und nichtlinearen Effekten.In der zweiten überarbeiteten und aktualisierten Auflage stellt der Autor niedrigdimensionale Modelle für Kristalle und Supergitter vor.

INTRODUCTION Geometry of crystal latticeCLASSICAL DYNAMICS OF A CRYSTAL LATTICE Mechanics of a one-dimensional crystal General analysis of vibrations of monoatomic lattices Vibrations of polyatomic lattices Frequency spectrum and its connection with the Green's function Acoustics of elastic ssuperlattices: Phonon crystalsQUANTUM MECHANICS OF CRYSTALS Quantization of crystal vibrations Interaction of excitations in a crystal Quantum crystalsDEFECTS Point defects Dislocations and disclinations Linear crystal defects Localization of vibrations Localization of vibrations near extended defects Elastic field of dislocations in a crystal Dislocation dynamics