Journal of Low Temperature Physics

, Volume 187, Issue 5–6, pp 692–698 | Cite as

Strong-Coupling Effects and Shear Viscosity in an Ultracold Fermi Gas



We theoretically investigate the shear viscosity \(\eta \), as well as the entropy density s, in the normal state of an ultracold Fermi gas. Including pairing fluctuations within the framework of a T-matrix approximation, we calculate these quantities in the Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensation (BEC) crossover region. We also evaluate \(\eta / s\), to compare it with the lower bound of this ratio, conjectured by Kovtun, Son, and Starinets (KSS bound). In the weak-coupling BCS side, we show that the shear viscosity \(\eta \) is remarkably suppressed near the superfluid phase transition temperature \(T_{\mathrm{c}}\), due to the so-called pseudogap phenomenon. In the strong-coupling BEC side, we find that, within the neglect of the vertex corrections, one cannot correctly describe \(\eta \). We also show that \(\eta / s\) decreases with increasing the interaction strength, to become very close to the KSS bound, \(\hbar /4\pi k_{\mathrm{B}}\), on the BEC side.


Ultracold Fermi gas BCS–BEC crossover Strong-coupling effect 



We would like to thank P. van Wyk, H. Tajima, R. Hanai, and D. Inotani for discussions. This work was supported by the KiPAS Project in Keio University. D.K. was supported by KLL Ph.D. Program Research Grant from Keio University. Y.O. was supported by Grant-in-Aid for Scientific Research from MEXT and JSPS in Japan (Nos. 15K00178, 15H00840, 16K05503).


  1. 1.
    S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 80, 1215 (2008)ADSCrossRefGoogle Scholar
  2. 2.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    L. Luo, J.E. Thomas, J. Low Temp. Phys. 154, 1 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    M.J.H. Ku, A.T. Sommer, L.W. Cheuk, M.W. Zwierlein, Science 335, 563 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    R. Haussmann, W. Rantner, S. Cerrito, W. Zwerger, Phys. Rev. A 75, 023610 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    C. Cao, E. Elliott, J. Joseph, H. Wu, J. Petricka, T. Schäfer, J.E. Thomas, Science 331, 58 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    J.A. Joseph, E. Elliott, J.E. Thomas, Phys. Rev. Lett. 115, 020401 (2015)ADSCrossRefGoogle Scholar
  9. 9.
    P.K. Kovtun, D.T. Son, A.O. Starinets, Phys. Rev. Lett. 94, 111601 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    E.W. Lemmon, M.O. McLinden, D.G. Friend, Thermophysical properties of fluid systems. In NIST Chemistry WebBook, NIST Standard Reference Database Number 69, ed. by P.J. Linstrom, W.G. Mallard (National Institute of Standards and Technology, Gaithersburg, 2016). Retrieved 17 July 2016
  11. 11.
    E. Elliott, J.A. Joseph, J.E. Thomas, Phys. Rev. Lett. 113, 020406 (2014)ADSCrossRefGoogle Scholar
  12. 12.
    S. Tsuchiya, R. Watanabe, Y. Ohashi, Phys. Rev. A 80, 033613 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    S. Tsuchiya, R. Watanabe, Y. Ohashi, Phys. Rev. A 82, 033629 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    S. Tsuchiya, R. Watanabe, Y. Ohashi, Phys. Rev. A 84, 043647 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    R. Watanabe, S. Tsuchiya, Y. Ohashi, Phys. Rev. A 82, 043630 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    A. Perali, F. Palestini, P. Pieri, G.C. Strinati, J.T. Stewart, J.P. Gaebler, T.E. Drake, D.S. Jin, Phys. Rev. Lett. 106, 060402 (2011)ADSCrossRefGoogle Scholar
  17. 17.
    A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (Dover Publications, New York, 2003)MATHGoogle Scholar
  18. 18.
    G.M. Bruun, H. Smith, Phys. Rev. A 75, 043612 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    E. Taylor, M. Randeria, Phys. Rev. A 81, 053610 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    T. Enss, R. Haussmann, W. Zwerger, Ann. Phys. 326, 770 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    A. Polyakov, Sov. Phys. JETP 30, 1164 (1970)ADSGoogle Scholar
  22. 22.
    A. Polyakov, Zh Eksp, Thor. Fiz. 57, 2144 (1969)Google Scholar
  23. 23.
    Y. He, K. Levin, Phys. Rev. B 89, 035106 (2014)ADSCrossRefGoogle Scholar
  24. 24.
    E.M. Lifshitz, L.P. Pitaevskii, Physical Kinetics, Course of Theoretical Physics (Pergamon Press, New York, 1981)Google Scholar
  25. 25.
    P. Massignan, G.M. Bruun, H. Smith, Phys. Rev. A 71, 033607 (2005)ADSCrossRefGoogle Scholar
  26. 26.
    G.M. Bruun, H. Smith, Phys. Rev. A 72, 043605 (2005)ADSCrossRefGoogle Scholar
  27. 27.
    G. Strinati, P. Pieri, C. Lucheroni, Euro. Phys. J. B 30, 161 (2002)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Physics, Faculty of Science and TechnologyKeio UniversityYokohamaJapan

Personalised recommendations