The Mathematical Theory of Thermodynamic Limits: Thomas-Fermi Type ModelsThe 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 This book presents new results, many previously unpublished, for a large class of models and provides a survey of the mathematics of thermodynamic limit problems.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. |
Contents
General Presentation | 1 |
Convergence of the energy for the ThomasFermivon | 34 |
Convergence of the energy for the ThomasFermivon | 85 |
Convergence of the density for the ThomasFermivon | 156 |
17 | 164 |
31 | 170 |
52 | 179 |
69 | 188 |
Convergence of the density for the ThomasFermivon | 194 |
80 | 220 |
91 | 226 |
Convergence of the energy via the convergence of | 228 |
| 272 | |
| 274 | |
Common terms and phrases
addition argument assume assumptions bounded Chapter charge convex Corollary Coulomb potential D(R³ deduce define definition denote dx dy electronic density energy per unit ETFW Euler-Lagrange equation exists fact goes to infinity goes to zero H¹(R³ H¹(To Harnack's inequality Hartree-Fock Hölder's inequality holds Hove sequence independent interior domains Iper ITFDW ITFW Lagrange multiplier Lieb lim inf Lunif R3 minimization problem minimizing density non-negative obtain Oper periodic boundary conditions periodic cell periodic function periodic lattice periodic potential point nuclei positive constant Pper proof of Lemma proof of Proposition prove quasicrystals recall Rellich's theorem Remark right-hand side sequence of interior smeared nuclei strategy of proof symmetry TER³ term TFDW TFW model thermodynamic limit Thomas-Fermi-von Weizsäcker u₁ unif uniform convergence uniformly uniqueness result unit cell unit cube unit volume YEZ3 Yukawa potential ΔΙ ΔΦ