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La Densité de niveaux du Problème à N-corps

Abstract : We investigate the many-body level density rho_MB for fermion and boson gases. We establish its behavior as a function of the temperature and the number of particules. We deal with correction terms due to finite number of particles effects for rho_MB : for fermions, it seems that it exists only one behavior whereas the case of bosons. Besides we propose a semiclassical expression of rho_MB for two types of particules with an angular momentum. It is decomposed into a smooth part coming from the saddle point method plus corrective terms due to the expansion of the number of partitions for two types of particles and an oscillating part coming from the fluctuations of the single-particle level density. Our model is validated by a numerical study. For the case of the atomic nucleus, the oscillating part of rho_MB is controled by a temperature factor which depends on the chaotic or integrable nature of the system and depends on the fluctuation of the ground state energy. This leads to consider in more detail this last quantity. For an isolated system, we give the general expression of the mean value for fixed potentials. We treat the self-bound system case through the example of the three dimensional harmonic oscillator (3DHO). Furthermore we study the oscillating part of rho_MB for bosons in the low temperature regime for billiards and for isotropic 3DHO. We note the oscillations disappear leading to a power law correction. In the case of the isotropic 3DHO, these corrections have the same order of magnitude as the smooth part. In the same way, for the high temperature regime we show the oscillating part of rho_MB is exponentially negligeable compared to the smooth part.
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Contributor : Jérôme Roccia <>
Submitted on : Thursday, October 4, 2007 - 4:40:30 PM
Last modification on : Wednesday, October 14, 2020 - 3:41:26 AM
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  • HAL Id : tel-00176867, version 1



Jerome Roccia. La Densité de niveaux du Problème à N-corps. Physique mathématique [math-ph]. Université Paris Sud - Paris XI, 2007. Français. ⟨tel-00176867⟩



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