# zbMATH — the first resource for mathematics

Thermodynamic limit for Thomas-Fermi type models. (Limite thermodynamique pour des modèles de type Thomas-Fermi.) (French. Abridged English version) Zbl 0849.35114
Summary: We present the proof of the existence of the thermodynamic limit for Thomas-Fermi-von Weizsäcker type models of molecules, in crystal case. We show that the ground state energy per unit volume converges to the ground state energy of some periodic minimization problem posed on the unit cell of the crystal. In addition, the ground state electronic density is shown to converge to the minimizing periodic density of the periodic problem. Various extensions are considered. In particular, we prove a result of existence and uniqueness of solutions of a system (of Schrödinger-Poisson type) of nonlinear elliptic partial differential equations.

##### MSC:
 35Q40 PDEs in connection with quantum mechanics 81V55 Molecular physics 82B30 Statistical thermodynamics