Böcker av Michel Le Bellac

This graduate-level text gives a self-contained exposition of fundamental topics in equilibrium and nonequilibrium statistical thermodynamics. The text follows a balanced approach between the macroscopic (thermodynamic) and microscopic (statistical) points of view. The first half of the book deals with equilibrium thermodynamics and statistical mechanics. In addition to standard subjects, the reader will find a detailed account of broken symmetries, critical phenomena and the renormalization group, as well as an introduction to numerical methods. The second half of the book is devoted to nonequilibrium phenomena, first following a macroscopic approach, with hydrodynamics as an important example. Kinetic theory receives a thorough treatment through analysis of the Boltzmann-Lorentz model and the Boltzmann equation. The book concludes with general nonequilibrium methods such as linear response, projection method and the Langevin and Fokker-Planck equations, including numerical simulations. This advanced textbook will be of interest to graduate students and researchers in physics.

Group action analysis developed and applied mainly by Louis Michel to the study of N-dimensional periodic lattices is the main 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 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 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 done through a number of concrete examples with an extensive use of graphical visualization. The book is addressed to graduated and post-graduate students and young researches in theoretical physics, dynamical systems, applied mathematics, solid state physics, crystallography, molecular physics, theoretical chemistry, ...