Thermodynamic limit for Thomas-Fermi type models

We present in this Note the proof of the existence of the thermodynamic limit for Thomas-Fernzi-von Weizsacker 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 Schrodinger-Poisson type) of nonlinear elliptic Partial Differential Equations.