Résumé (EN)

We prove Hohenberg-Kohn theorems for several models of quantum mechanics. First, we show that for possibly degenerate systems of several types of particles, the pair correlation functions of any ground state contain the information of the interactions and of the external potentials. Then, in the presence of the Zeeman interaction, a strong constraint on external fields is derived for systems having the same ground state densities and magnetizations. Next, we prove that the density and the entropy of a ground state contain the information of both the imposed external potential and temperature. Eventually, we conclude that at positive temperature, Hohenberg-Kohn theorems generically hold.