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.
Similar content being viewed by others
References
W. Ebeling and W. D. Kraeft,Theory of Bound States and lonization Equilibrium in Plasmas and Solids (Akademie-Verlag, Berlin, 1976); W. D. Kraeft, D. Kremp, W. Ebeling, and G. Ropke,Quantum Statistics of Charged Particle Systems (Akademie-Verlag, Berlin, 1986).
C. Fefferman,Rev. Math. Iberoam. 1:1 (1985).
J. G. Conlon, E. H. Lieb, and H. T. Yau,Commun. Math. Phys. 125:153 (1989).
N. Macris and Ph. A. Martin,J. Stat. Phys. 60:619 (1990).
J. L. Lebowitz and R. E. Penna,J. Chem. Phys. 59:1362 (1973).
W. D. Kraeft, D. Kremp, K. Kilimann, and H. E. De Witt,Phys. Rev. A 42:2340 (1990).
S. Ichimaru, ed.,Strongly Coupled Plasma Physics, Proceedings of the Yamada Conference XXIV (Elsevier, Amsterdam, 1990).
M. D. Girardeau,Phys. Rev. A 41:6935 (1990).
N. Macris, Ph. A. Martin, and J. V. Pule,Helv. Phys. Acta 63:705 (1990).
J. M. H. Levelt and E. G. D. Cohen, inStudies in Statistical Mechanics, Vol. II, J. de Boer and G. E. Uhlenbeck, eds. (North-Holland, Amsterdam, 1964), Chapter 4, p. 142.
M. D. Girardeau, inStrongly Coupled Plasma Physics, Proceedings of the Yamada Conference XXIV, S. Ichimaru, ed. (Elsevier, Amsterdam, 1990).
H. Kunz and B. Souillard,Commun. Math. Phys. 78:201 (1980); I. M. Lifshits and L. A. Pastur,Introduction to the Theory of Disordered Systems (Wiley, New York,1988).
B. Simon,Functional Integration and Quantum Physics (Academic Press, 1979).
T. Kato,Perturbation Theory for Linear Operators (Springer-Verlag, 1984).
H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon,Schrödinger Operators with Applications to Quantum Mechanics and Global Geometry (Springer-Verlag, 1987).
M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. IV,Analysis of Operators (Academic Press, 1978).
M. Klaus,Helv. Phys. Acta 55:49 (1982).
M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. II,Fourier Analysis, Self Adjointness (Academic Press, 1975).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lebowitz, J.L., Macris, N. & Martin, P.A. Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: A model study. J Stat Phys 67, 909–956 (1992). https://doi.org/10.1007/BF01049005
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01049005