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Contribution à la Théorie des Gaz Dilués-Dégénérés

Abstract : We present a new theoretical approach to describe dilute degenerate gases, the formalism of Ursell operators. The partition function of a quantum gas is obtained in two steps: first, we account for the interaction in an auxiliary system of distinguishable particles, making use of a low density approximation (the ratio between potential range and average interparticle spacing is assumed to be very small). In a second stage, quantum statistics are introduced; no approximations whatsoever are necessary in this step, which allows for the treatment of degenerate systems. It is possible to derive expressions for reduced density operators from the thermodynamical potential. We are thus able to study macroscopic systems on a microscopic scale. An expression for the two-particle correlation function of a system of hard spheres is obtained which reproduces the "good" physical properties even at short relative distances. This presents a great advantage compared to usual methods of mean field theories. We determine formulae for a variety of macroscopic quantities in an approximation which is valid for systems at low density (generalized Beth-Uhlenbeck formula). The interaction potential enters into these expressions by the means of a new parameter, the Ursell length. We compare our results to those of the pseudopotential theory and show that the latter gives a correct image of the physical phenomena for bosons. For fermions, however, we find an important difference: at sufficently low temperatures even entirely repulsive potentials give rise to an effective attraction. We also made a numerical study of the dependence on density of the critical temperature of Bose-Einstein condensation in a bosonic hard sphere gas. Our calculus of path integrals by Monte Carlo methods shows that the critical temperature is increased compared to that of the ideal gas at low density (by a factor of 1.07 at most).
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https://tel.archives-ouvertes.fr/tel-00011907
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Submitted on : Friday, March 10, 2006 - 9:02:45 AM
Last modification on : Monday, December 14, 2020 - 9:51:14 AM
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  • HAL Id : tel-00011907, version 1

Citation

Peter Gruter. Contribution à la Théorie des Gaz Dilués-Dégénérés. Physique Atomique [physics.atom-ph]. Université Paris Sud - Paris XI, 1996. Français. ⟨tel-00011907⟩

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