Relativistic Superfluid In The Bcs-bec Conversion

We investigate the crossover from Bardeen-Cooper-Schrieffer(BCS)pairing to a Bose-Einstein condensate(BEC)in a relativistic superfluid within a boson-fermion model.The model includes,besides the fermions,separate bosonic degrees of free-dom,accounting for the bosonic nature of the Cooper pairs.The crossover is realized by tuning the difference between the boson mass and boson chemical potential or directly the bare boson mass as a free parameter.As a mean field approxima-tion(MFA),we neglect the coupling between the thermal bosons with the fermions, the model yields populations of condensed and uncondensed bosons as well as gapped and ungapped fermions throughout the crossover region for arbitrary temperatures. Moreover,we observe the appearance of antiparticles for sufficiently large values of the crossover parameter.As an application,we study pairing of fermions with im-balanced populations and find the disappearing of the stable solution in the strong coupling region.To go beyond the MFA we use Cornwall-Jackiw-Tomboulis(CJT)formalism to include higher order contributions.The quantum fluctuations of the pairing condensate is provided by bosons in non-zero modes,whose interaction with fermions gives the two-particle-irreducible(2PI)effective potential.It changes the crossover property in the BEC regime.We calculate the condensate,the critical temperature T_c and particle abundances as functions of crossover parameter the squared boson mass.We also compute the dissociation temperature T* for bosons,above which they are not stable and start to decay.We find the crossover parameter range for T~*＞T_c,which indicates the existence of bosons even above T_c but below T~*.The model can potentially be applied to color superconductivity in dense quark matter at strong couplings.Or it can be extended to discuss the quarkoyinic conti-nuity.The main innovations in this thesis are listed below:●For the first time,we investigate the crossover from BCS pairing to a BEC in a relativistic superfluid within a boson-fermion model. ●In mean field approximation,the model yields populations of condensed and uncondensed bosons as well as gapped and ungapped fermions throughout the crossover.●We observe the appearance of antiparticles for sufficiently large coupling as a characteristic of relativistic model.●We study the pairing of fermions with imbalanced populations in BCS-BEC crossover,and find the disappearing of the stable solution in the strong coupling region.●We also study the fluctuation effect in the crossover and find the parameter region for stable bosons where T~*＞T_c.