Universität Potsdam Institut für Physik KarlLiebknechtStr. 24/25 14476 PotsdamGolm 



AbstractWe consider a dilute homogeneous mixture of bosons and spinpolarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green's functions. We especially focus on the description of the bosonfermion interaction. To do so we need to introduce a new relevant object, the renormalized bosonfermion Tmatrix which we determine to second order in the bosonfermion swave scattering length. We also discuss how to incorporate the usual bosonboson Tmatrix in mean field approximation to obtain the total ground state properties of the system. The next order term beyond mean field stems from the bosonfermion interaction and is proportional to a_{BF}k_{F}. The total ground state energy density to this order is the sum of the kinetic energy of the free fermions, the bosonboson mean field interaction, the usual meanfield contribution to the bosonfermion interaction energy, and the first bosonfermion correction beyond mean field. We also compute the bosonic and the fermionic chemical potentials, the compressibilities, and the modification to the induced fermionfermion interaction. We discuss the behavior of the total ground state energy and the importance of the correction beyond mean field for various parameter regimes, in particular considering mixtures of ^{6}Li and ^{7}Li and of ^{3}He and ^{4}He. Moreover, we determine the modification of the induced fermionfermion interaction due to the effects beyond mean field. We show that there is no effect on the depletion of the Bose condensate to first order in the bosonfermion scattering length a_{BF}. file generated: 5 Jun 2008


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