Generalized One-Particle Density Matrices and Quasifree States
Mathematical Physics
2014-01-14 v1 math.MP
Abstract
In the spirit of the generalized one-particle density matrix for fermions, we introduce generalized one- and two-particle density matrices to state representability conditions up to second order for boson systems without assuming particle number-conservation. Furthermore, we show for both particle species that, for a semibounded Hamiltonian, the in?mum of the variation of the energy functional w.r.t quasifree states coincides with the one of a variation over pure quasifree states. Moreover, it is proven for fermions that only pure quasifree states have a generalized 1-pdm that is a projection, and a similar statement for bosons.
Cite
@article{arxiv.1304.7995,
title = {Generalized One-Particle Density Matrices and Quasifree States},
author = {Volker Bach and Sébastien Breteaux and Hans Konrad Knörr and Edmund Menge},
journal= {arXiv preprint arXiv:1304.7995},
year = {2014}
}