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 This book presents new results, many previously unpublished, for a large class of models and provides a survey of the mathematics of thermodynamic limit problems.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 Weizsäcker model with Yukawa potential


• 3: Convergence of the energy for the Thomas-Fermi-von-Weizsäcker model


• 4: Convergence of the density for the Thomas-Fermi-von-Weizsäcker model with Yukawa potential


• 5: Convergence of the density for the Thomas-Fermi-von-Weizsäcker model


• 6: Convergence of the energy via the convergence of the density


• Bibliography