Relativistic BCS-BECcrossoverRecentworksbyothergroup:Nishida&Abuki,PRD20o7--NJLapproachAbuki,NPA2oo7-StaticandDynamicpropertiesSun,He&Zhuang,PRD2oo7-NJLapproachHe&Zhuang,PRD2007-BeyondmeanfieldKitazawa,Rischke&Shovkovy,arXiv:0709.2235v1NJL+phasediagramBrauner,arXiv:0803.2422-Collectiveexcitations
Relativistic BCS-BEC crossover Recent works by other group: • Nishida & Abuki, PRD 2007 - NJL approach • Abuki, NPA 2007 – Static and Dynamic properties • Sun, He & Zhuang, PRD 2007 – NJL approach • He & Zhuang, PRD 2007 – Beyond mean field • Kitazawa, Rischke & Shovkovy, arXiv:0709.2235v1 – NJL+phase diagram • Brauner, arXiv:0803.2422 – Collective excitations
Boson-fermion model (MFA)With bosonic and fermionic degrees of freedom with MeanField Approximation.-1 +[μ - m]02 + [(0t- iμb)2 - /V|2 - ml122亚=(,亚c)1Pμ+μo-m2ig5*S-1(P)2ig5Pμu-μo-m△ = 2gΦ,Non-relativisticversion:Friedberg,Lee,PRB1989Friedberg,Lee,Ren,PRB1990
Boson-fermion model (MFA) With bosonic and fermionic degrees of freedom with Mean Field Approximation. Non-relativistic version: Friedberg, Lee, PRB 1989 Friedberg, Lee, Ren, PRB 1990
Thermodynamic potetial1/T2[dv][d][dp][d*] expPccdTOOEko = Vk2 + m2x = V(eko - ep)2 + 42(m -)2we= Vk2+m-eb24g2d3k# +2TIn [1+exp(-)])Z（2元）3e=士d3kZ[u +2Tin [1- exp(-等)]]12(2元)3
Thermodynamic potetial
Density and gap equations02(μ,△nnF + nB二nOpd3kck11Ztanh02(μ,△)-X二(2元)32e2T2eko0e=±00mb, - μbX三Crossoverparameter4g2(μ, △)
Density and gap equations Crossover parameter