J. Phys. I France
Volume 5, Numéro 10, October 1995
Page(s) 1255 - 1279
DOI: 10.1051/jp1:1995196
J. Phys. I France 5 (1995) 1255-1279

Ursell Operators in Statistical Physics II: Microscopic Properties of a Dilute Quantum Gas

P. Grüter and F. Laloë

Laboratoire Kastler Brossel de l'ENS, Unité associée au CNRS UA-18 et à l'Université Pierre et Marie Curie, France

(Received 7 April 1995, accepted 20 June 1995)

We apply the formalism of Ursell operators, introduced in a previous article, to the calculation of reduced density operators (one and two-body density operators) in a dilute quantum gas; the calculation is not a fugacity expansion and is therefore not limited to low degrees of degeneracy. We obtain quantum corrections for the one-particle density operator as a function of the second Ursell operator. For the two-body density operator, we examine how statistics and interactions combine their effects on the correlations between particles; in particular we discuss in detail how hard cores potentials affect the short range correlations, a non-perturbative effect.

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