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Contribution à la théorie des gaz de fermions froids

Abstract : This thesis deals with the N body problem in ultra cold Fermi gases. The first part presents collisions between 3 and 4 fermions in contact interaction in vacuum. We show how to calculate diagrammaticaly the dimer-fermion scattering amplitude and the dimer-dimer scattering length. Using a development in power of the mass ratio, we get an analytical expression for the dimer-fermion s wave scattering amplitude in the large mass ratio limit between two species. Using the same method, we get an analytical expression for the dimer-dimer s wave scattering length in the large mass ratio limit between two species. In the second part, we consider the many body problem in the BEC-BCS crossover. We derive the Tan's formula for the energy in the contact interaction limit, then we generalize this result for bosonic mixtures and for 2 dimensions systems. We also calculate the equation of state at unitarity with the T matrix approximation using 3 exact formulas for the energy. Finally, we obtain a development for the equation of state in the BEC limit in power of the density. The result is obtained, in the general case where two species have different masses and unequal numbers, by considering diagrammaticaly the exact 3 and 4 body vertices.
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Contributor : Florent Alzetto <>
Submitted on : Friday, April 5, 2013 - 9:37:01 AM
Last modification on : Thursday, October 29, 2020 - 3:01:24 PM
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  • HAL Id : tel-00808195, version 1

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Florent Alzetto. Contribution à la théorie des gaz de fermions froids. Gaz Quantiques [cond-mat.quant-gas]. Université Pierre et Marie Curie - Paris VI, 2011. Français. ⟨tel-00808195⟩

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