The Mathematical Theory of Thermodynamic Limits Thomas--Fermi Type Models [Hardcover]

The thermodynamic limit is a mathematical technique for modeling crystals or other macroscopic objects by considering them as infinite periodic arrays of molecules. The technique allows models in solid state physics to be derived directly from models in quantum chemistry. This book presents new results, many previously unpublished, for a large class of models and provides a survey of the mathematics of thermodynamic limit problems. The authors both work closely with Fields Medal-winner Pierre-Louis Lion, and the book will be a valuable tool for applied mathematicians and mathematical physicists studying nonlinear partial differential equations.

Preface
Contents
1. General Presentation
2. Convergence of the energy for the Thomas-Fermi-von Weizs?cker model with Yukawa potential
3. Convergence of the energy for the Thomas-Fermi-von-Weizs?cker model
4. Convergence of the density for the Thomas-Fermi-von-Weizs?cker model with Yukawa potential
5. Convergence of the density for the Thomas-Fermi-von-Weizs?cker model
6. Convergence of the energy via the convergence of the density
Bibliography

Indeed, while motivated by questions from physics or chemistry, in this book the focus is definitely on the mathematical aspects and methods of solving the problems studied. With this work, a significant step in the rigorous treatment of the thermodynamic limit is accomplished. A fine piece of mathematical physics presented by the original authors in a pedagogical way, in this sense the book is certainly an outstanding contribution to the literature. -Mathematical Reviews