Atomic versus Ionized States in Many-Particle Systems and the Spectra of Reduced Density Matrices: A Model Study

We study the spectrum of appropriate reduced density matrices for a model consisting of one quantum particle ("electron") in a classical fluid (of "protons") at thermal equilibrium. The quantum and classical particles interact by a shortrange, attractive potential such that the quantum particle can form "atomic" bound states with a single classical particle. We consider two models for the classical component: an ideal gas and the "cell model of a fluid." We find that when the system is at low density the spectrum of the "electron-proton" pair density matrix has, in addition to a continuous part, a discrete part that is associated with "atomic" bound states. In the high-density limit the discrete eigenvalues disappear in the case of the cell model, indicating the existence of pressure ionization or a Mott effect according to a general criterion for characterizing bound and ionized electron-proton pairs in a plasma proposed recently by M. Girardeau. For the ideal gas model, on the other hand, eigenvalues remain even at high density.