Weak Interaction p-Wave Superfluid Fermi Gas: Low-Temperature Shear Viscosity

Document Type : Original Research Articles

Authors
Soudabe Nasirimoghadam 1
Roohollah Aliabadi 1
Mohammad Ali Shahzamanian 2
1 1 Department of Physics, Sirjan University of Technology, Sirjan 78137, Islamic Republic of Iran
2 2 Department of Physics, Faculty of Sciences, University of Isfahan, Isfahan 81744, Islamic Republic of Iran
10.22059/jsciences.2023.347342.1007748
Abstract
The shear viscosity tensor of a superfluid Fermi gas in a p-wave state with weak interactions was investigated using the Boltzmann equation at low temperatures. Therefore, transition probabilities of the binary collision, decay, and coalescence processes were considered for this purpose. Theoretically, the dominant processes at low temperatures find to be the binary ones, whereas the elements of the shear viscosity (i.e., ) report to be proportional to . Moreover, behaved as , and  was proportional to .
Keywords
Superfluid, Fermi gas
Shear viscosity
Subjects
  1. You L, Marinescu M. Prospects for p-wave paired Bardeen-Cooper-Schrieffer states of fermionic atoms. Physic Rev A. 1999;60(3):2324-2329.
  2. Combescot R. Trapped 6Li: a high superfluid. Physic Rev Lett. 1999; 83(19):3766-3769.
  3. Zhang W, Sá de Melo CARS. Matter-wave interference in s-wave and p-wave Fermi condensates. Physic Rev A. 2007;76(1):013627.
  4. Zhang J, van Kempen EGM, Bourdel T, Khaykovich L, Cubizolles J, Chevy F, et al. P-wave Feshbach resonances of ultracold 6Li. Physic Rev A. 2004;70(3):030702.
  5. Ho TL, Diener RB. Fermion superfluids of nonzero orbital angular momentum near resonance. Physic Rev Lett. 2005;94(9):090402.
  6. Nozieres P, Schmitt-Rink S. Bose condensation in an attractive fermion gas: from weak to strong coupling superconductivity. J Low Temperat Physics. 1985;59(3):195-211.
  7. Leggett AJ. Bose-Einstein condensation in the alkali gases: some fundamental concepts. Rev Modern Physics. 2001;73(2):307-356.
  8. Ku MJH, Sommer AT, Cheuk LW, Zwierlein MW. Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas. Science. 2012;335(6068):563-567.
  9. Hu H, Yao XC, Liu XJ. Second sound with ultracold atoms: a brief review. AAPPS Bulletin. 2022; 32(26):1-25.
  10. Bruun GM, Smith H. Viscosity and thermal relaxation for a resonantly interacting Fermi gas. Physic Rev A. 2005;72(4):043605.
  11. Joseph JA, Elliott E, Thomas JE. Shear viscosity of a unitary Fermi gas near the superfluid phase transition. Physic Rev Lett. 2015; 115(2):020401.
  12. Massignan P, Bruun GM, Smith H. Viscous relaxation and collective oscillations in a trapped Fermi gas near the unitarity limit. Physic Rev A. 2005;71(3):033607.
  13. Bruun GM, Smith H. Shear viscosity and damping for a Fermi gas in the unitarity limit. Physic Rev A. 2007;75(4):043612.
  14. Shahzamanian MA, Yavari H. The shear viscosity of superfluid 6Li. Physica B. 2002;321(1-4):385-387.
  15. Shahzamanian MA, Yavari H. The shear viscosity of a trapped Bose-condensed gas. Ann Physics. 2006;321(5):1063-1074.
  16. Dusling K, Schäfer T. Bulk viscosity and conformal symmetry breaking in the dilute Fermi gas near unitarity. Physic Rev Lett. 2013;111(12):120603.
  17. Rupak G, Schäfer T. Shear viscosity of a superfluid Fermi gas in the unitarity limit. Physic Rev A. 2007;76(5):053607.
  18. Cao C, Elliott E, Joseph J, Wu H, Petricka T, Schäfer T, et al. Universal quantum viscosity in a unitary Fermi gas. Science. 2011;331(6013):58-61.
  19. Bluhm M, Hou J, Schäfer T. Determination of the density and temperature dependance of the shear viscosity of a unitary Fermi gas based on hydrodynamic flow. Physic Rev Lett. 2017;119(6):065302.
  20. Zhou H, Dong H, Ma Y. Scattering mechanisms, relaxation times, and shear viscosity in universal anomalous transport of unitary Fermi gases. Physic Rev Res. 2020;2(2):023166.
  21. Enss T, Haussmann R, Zwerger W. Viscosity and scale invariance in the unitary Fermi gas. Ann Physics. 2011;326(3):770-796.
  22. Taylor E, Randeria M. Viscosity of strongly interacting quantum fluids: spectral functions and sum rules. Physic Rev A. 2010;81(5):053610.
  23. Kagamihara D. Inotani D. Ohashi Y. Shear viscosity and strong-coupling corrections in the BCS–BEC crossover regime of an ultracold Fermi gas. J Physic Soc Jpn. 2019;88(11):114001.
  24. Guo H, Wilin D, Chien CC, Levin K. Microscopic approach to shear viscosities of unitary Fermi gases above and below the superfluid transition. Physic Rev Lett. 2011;107(2):020403.
  25. Sykes J, Brooker GA. The transport coefficients of a fermi liquid. Ann Physics. 1970;56(1):1-39.
  26. Tilley DR, Tilley J. Superfluidity and Superconductivity. (Adam Hilger, Bristol & Boston, 1986).
  27. Takagi S. On the NMR properties near the 3He A-normal transition. J Low Temperat Physics. 1975;18(3):309-314.
  28. Shahzamanian MA, Afzali R. Shear viscosity of superfluid 3He–A1 at low temperatures. Ann Physics. 2004;309(2):281-294.
  29. Volhardt D, Wölfle P. The Superfluid Phases of Helium 3. (Taylor & Francis, London, 1990).
  30. Shahzamanian MA. Diffusive thermal conductivity of superfluid 3He-A at low temperatures. J Physics: Condenses Matter. 1989;1(11):1965-1970.
  31. Pethick CJ, Smith H. Bose-Einstein Condensation in Dilute Gases. (Combridge University Press, Combridge, 2002).
  32. Pfitzner MP. General polynomial expansion of the quasiparticle scattering amplitude in normal Fermi fluids. Journal of Low Temperature Physics. 1985;61(1):141-154.
  33. Mortimer CE. Chemistry Charles E. Mortimer. (Wadsworth, 1986).

 
  1. Pines D, Nozieres P. The Theory of Quantum Liquids. (Benjamin, Newyork, 1966).
  2. Shahzamanian MA. A microscopic calculation of the fourth-rank shear viscosity tensors of superfluid phases of 3He. Journal of Physics C: Solid State Physics. 1988;21(3):553.
  3. Roobol LP, Remeijer P, Steel SC, Jochemsen R, Shumeiko VS, Frossati G. Shear viscosity of superfluid 3He up to 15 Tesla. Physic Rev Lett. 1997;79(4):685-688.
  4. Schäfer T. Shear viscosity and damping of collective modes in a two-dimensional Fermi gas. Physic Rev A. 2012;85(3):033623.
Journal of Sciences, Islamic Republic of Iran
Volume 34, Issue 2
Spring 2023
Pages 149-156