HohenbergKohn Theorems for Interactions, Spin and Temperature
Abstract
We prove HohenbergKohn 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. Also, we provide a counterexample in a setting involving nonlocal potentials. 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, HohenbergKohn theorems generically hold, in particular they hold in the classical case.
 Publication:

Journal of Statistical Physics
 Pub Date:
 November 2019
 DOI:
 10.1007/s10955019023656
 arXiv:
 arXiv:1906.03191
 Bibcode:
 2019JSP...177..415G
 Keywords:

 Mathematical physics;
 Quantum physics;
 Statistical physics;
 Density functional theory;
 HohenbergKohn theorems;
 Mathematical Physics;
 Condensed Matter  Statistical Mechanics;
 Quantum Physics
 EPrint:
 Journal of Statistical Physics (2019)