1. Relativistic BCS-BEC Crossover in a boson-fermion Model
Qun Wang
University of Science and Technology of China
Motivation
Boson-fermion Model
Results and discussion
Summary and outlook
Deng, Schmitt, QW, Phys.Rev.D76:034013,2007
Deng, Wang, QW, arXiv:
10th workshop for particle physics, Nanjing, April 2008

2. Color superconductivity in neutron stars

3. Strongly Coupled Quark Gluon Plasma In Relativistic Heavy Ion Collisions

4. BCS-BEC Crossover
Science

5. BCS-BEC Crossover

6. Relativistic BCS-BEC crossover
Recent works by other group:
Nishida & Abuki, PRD NJL approach
Abuki, NPA 2007 – Static and Dynamic properties
Sun, He & Zhuang, PRD – NJL approach
He & Zhuang, PRD 2007 – Beyond mean field
Kitazawa, Rischke & Shovkovy, arXiv: v1 – NJL+phase diagram
Brauner, arXiv: – Collective excitations

7. 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

8. Thermodynamic potetial

9. Density and gap equations
Crossover parameter

10. At zero T or critical T

11. Dispersion relation
In BCS regime, fermions are slightly gapped, anti-fermions are strongly gapped. In BEC regime, both are strongly gapped, indicating the formation of bound states with large binding energy

12. Finite T BCS regime: Melting condensation of fermion pairs
BEC regime: Melting condensation of bosons

13. Pairing with imbalance population
Alford, Berges & Rajagopal, PRL 2000; Alford, Kouvaris & Rajagopal, PRL 04, PRD Gapless and crystalline color superconductivity
Huang, Shovkovy, PLB 2003 and NPA 2003; PRD 04; PRD Gapless color superconductivity in 2SC, instablility in Meissner masses
Many others ……

14. Fermi surface topologies

15. Homogeneous solution
We use the number susceptibility to tell which solution are stable.

16. Phase diagram

17. The fluctuation of condensate CJT formalism
Cornwall, Jackiw, Tomboulis, PRD 1974

18. 2PI diagrams and DS equations

19. Pseudo-gap (1)

20. Pseudo-gap (2)

21. Gap & Density equations

22. The results are similar to the MFA results
At small T
The results are similar to the MFA results

23. At T=Tc
Fluctuations become important in BEC regime. In BEC regime T*>Tc.

24. With increasing T
The fluctuation effects become larger. BEC criterion is related to the minimization of the thermodynamics potential.

25. Summary
Describe BCS-BEC crossover within or beyond MFA. Crossover parameters x and mb2 are equivalent. Due to relativistic feature, antiparticle must be present. With chemical potential mismatch, some homogeneous solution are unstable, LOFF or heterogeneous phases should be considered. Fluctuation affects the crossover properties in high temperature and strong coupling. BEC criterion is related to the minimization of the thermodynamics potential.

26. Outlook
Our model can be extended to discuss quarkoynic continuity with finite chemical potential where the confinement and chiral symmetry breaking are not coincide (L. Mclerran and R. D. Pisarski ). BEC criterion for interacting bosons need more close look. Full self-consistency is needed.