Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: A model study |
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Authors: | Joel L Lebowitz Nicolas Macris Philippe A Martin |
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Institution: | (1) Department of Mathematics and Physics, Rutgers University, 08903 New Brunswick, New Jersey;(2) Institut de Physique Théorique, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland |
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Abstract: | 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. |
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Keywords: | Bound and ionized states Mott effect pressure ionization reduced density matrix discrete and continuous spectra functional integrals Birman-Schwinger principle |
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