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BCS-BEC Crossover in Relativistic System and Possible Realization in QCD

This paper discusses the BCS-BEC crossover theory in relativistic systems, both at zero and finite temperature. It also explores the possibility of BCS-BEC crossover in diquark and isospin matter. The size of quark pseudogap in chiral and color superconductivity phase transitions is calculated.

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BCS-BEC Crossover in Relativistic System and Possible Realization in QCD

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  1. BCS-BEC Crossover in Relativistic System and Its Possible Realization in QCD Lianyi He and Pengfei Zhuang Physics Department, Tsinghua U. References:Phys.Rev.D75:096003,2007 Phys.Rev.D75:096004,2007 Phys.Rev.D76:056003,2007 E-print Arxiv: 0709.2246 ATHIC2008, TSUKUBA, JAPAN

  2. Impact of Superconductivity ATHIC2008, TSUKUBA, JAPAN

  3. BCS BEC Theoretical History of Crossover: Introduction to BCS-BEC Crossover • Leggett (1980) noted that BCS T=0 wavefunction could be • generalized to arbitrary attraction: a smooth BCS-BEC crossover ! weak coupling strong coupling ATHIC2008, TSUKUBA, JAPAN

  4. Eagles (1969): Pairing without superconductivity In HTSC, the root of PG is not quite clear. The pre-formed boson mechanism is only one explanation. ATHIC2008, TSUKUBA, JAPAN

  5. Experimental evidence for pseudogap in ultracold fermions Science 305, 1128 (2004) Science 307, 1296 (2005) ATHIC2008, TSUKUBA, JAPAN

  6. T m Relativistic BCS-BEC Crossover Motivation: 1) QCD phase diagram at moderate temperature and density, strong coupling nature! 2) BCS-BEC crossover in CSC? Pseudogap of CSC 3) NJL model: BCS theory of chiral symmetry breaking. Chiral pesudogap above Tc? Quark Spectrum and pseudogap, M. Kitazawa, et.al. 2005 SQGP? Structure change of Cooper pairs, H.Abuki, et.al.2002 pseudogap? SB CSC BEC? ATHIC2008, TSUKUBA, JAPAN

  7. Progress in this field of research H.Abuki and Y.Nishida: NSR approach, new crossover: BCS-BEC-RBEC L.He and P.Zhuang: BCS-Leggett theory at zero T and pesudogap theory at finite T BCS-BEC vs. Chiral Restoration J.Deng and Q.Wang: Boson-fermion model in mean field and beyond mean field M.Kitazawa, D.Rischke and I.Shovkovy: Possible Diquark BEC in NJL T.Brauner: Collective Excitation 1/N expansion including quantum fluctuation (with H.Abuki)

  8. Zero Temperature: BCS-Leggett mean Field Theory Model Lagrangian Mean Field Equations ATHIC2008, TSUKUBA, JAPAN

  9. Fermionic Excitation Spectrum fermion anti-fermion • Non-relativistic limit • Criterion for BCS and BEC: Minimum of the dispersion • BCS: at , existence of Fermi surface • BEC: at , molecule condensation • The role of fermion mass (new aspect in QCD) • BCS-BEC Chiral symmetry breaking& restoration ATHIC2008, TSUKUBA, JAPAN

  10. The Non-Relativistic Limit For small value of the parameter , the NR version of BCS-Leggett result is recovered The condition or is needed ATHIC2008, TSUKUBA, JAPAN

  11. Relativistic Effect I: BCS-NBEC-RBEC Crossover Physical picture: RBEC: , anti-particles available! ATHIC2008, TSUKUBA, JAPAN

  12. Relativistic Effect II: Density Induced Crossover ATHIC2008, TSUKUBA, JAPAN

  13. Collective Mode Evolution Effective action Dispersion of the collective mode Goldstone mode A-B mode BCS NBEC Bogoliubov theory RBEC Ultra-relativistic BEC ATHIC2008, TSUKUBA, JAPAN

  14. Nonzero Temperature: Pseudogap theory K.Levin and Qijin Chen, et.al, Phys.Rept. 412, 1(2005) ATHIC2008, TSUKUBA, JAPAN

  15. Tc Calculation NBEC regime RBEC regime Bound states above Tc ATHIC2008, TSUKUBA, JAPAN

  16. BCS-BEC Crossover in QCD? Two color QCD QCD at finite isospin density In the BEC region, quark energy gap is different from the order parameter! Can be confirmed in Lattice! Phys.Rev.D75:096004,2007 ATHIC2008, TSUKUBA, JAPAN

  17. Chiral restoration vs. BCS-BEC crossover BEC BCS ATHIC2008, TSUKUBA, JAPAN

  18. Pseudogap in QCD? Condensation and Chiral Phase Transition NJL Model Nc dependence Quark mass is still large above chiral phase transition! ATHIC2008, TSUKUBA, JAPAN

  19. Diquark condensation and color superconductivity NJL model, 2SC phase Quark pesudogap remarkable! A high Tc superconductor! ATHIC2008, TSUKUBA, JAPAN

  20. Non-Fermi liquid behavior at low T! (High T, see M.Kitazawa, 2005)

  21. Summary 1. BCS-BEC crossover theory has been generalized to relativistic system, both at zero and at finite temperature. 2. Proper NR limit is recovered and new relativistic effects are found. 3. Possible BCS-BEC crossover in diquark and isospin matter is discussed. 4. The size of quark pseudogap in chiral and CSC phase transition is calculated. Outlook • Determine the pseudogap phase in QCD phase diagram • Signals of diquark fluctuation and pesudogap in HIC • Effect of the pseudogap on compact star cooling • More precise theory, including quantum fluctuation ATHIC2008, TSUKUBA, JAPAN

  22. Thank You! ATHIC2008, TSUKUBA, JAPAN

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