Fluidity of the medium is measured by the shear viscosity to entropy density ratio η/s. Being roughly proportion to the ratio of mean free path to de-Broglie wavelength of medium constituents, the η/s of any fluid never be vanished because mean free path of constituents can not be lower than their de-Broglie wavelength. So it indicates that quantum fluctuations prevent the existence of perfect fluids in nature and η/s has a quantum lower bound, which is also claimed by the calculation from ADS/CFT correspondence. In 2002, researchers at Duke university discovered a super-cold lithium fluid having very small η/s (< 0.5), close to the lower bound whereas, three years latter, RHIC experiment created a super-hot QGP fluid with smallest η/s, almost equal to the lower bound. This nearly perfect fluid nature of many body system at two extreme conditions (super-cold and super-hot) has attracted the attention of large band of theoretical communities from condense matter physics to nuclear physics to String theory.
The hydrodynamical calculations became very successful in explaining the elliptical flow parameter v2 from RHIC data only when they assumed a very small ratio of shear viscosity to entropy density (η/s) for the expanding nuclear matter. See :
- P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99, 172301 (2007).
- M. Luzum and P. Romatschke, Phys. Rev. C 78, 034915 (2008).
- H. Song and U. W. Heinz, Phys. Lett. B 658, 279 (2008).
- H. Song and U. W. Heinz, Phys. Rev. C 78, 024902 (2008).
- V. Roy, A. K. Chaudhuri, and B. Mohanty, Phys. Rev. C 86, 014902 (2012).
- H. Niemi, G. S. Denicol, P. Huovinen, E. Molnar, and D. H. Rischke, Phys. Rev. C 86, 014909 (2012).
- B. Schenke, S. Jeon, and C. Gale, Phys. Rev. C 85, 024901 (2012).
This experimental values of η/s, based on RHIC data, is approximately 10-20 times smaller than the values obtained from traditional perterbative QCD (pQCD) or hard thermal loop (HTL) calculation. This discrepancy motivates several model dependent microscopic calculation of η/s for alternative understanding of QCD medium. But we notice that estimated values of different investigations are located in a quite large numerical band.
A high-temperature, weakly interacting medium is naturally expected to be produced in heavy ion collision (HIC) experiments at high energies because the constituents of the medium (quarks and gluons) should become almost free according to the asymptotic freedom property of QCD.
In this context, some of my collaborative research have started
- in my PhD Institute VECC ( http://www.vecc.gov.in/ ) : Effect of spectral modification of
ρ on shear viscosity of a pion gas; S. Mitra, Sabyasachi Ghosh (VECC, Kolkata, India), S. Sarkar; Published in Phys. Rev. C 85, 064917 (2012)................. Here, we have mainly interested to observe how a dressed rho meson propagator in the pi-pi scattering diagrams make impact on shear viscosity of hadronic matter. We have used the in-medium rho propagator for mesonic loops only, whose detail calculations are addressed in our earlier work : Analytic structure of rho meson propagator at finite temperature; Sabyasachi Ghosh, S. Sarkar, S. Mallik; Published in Eur. Phys. J. C 70 (2010) 251. - in my Post PhD period (from Nov, 2012 to March, 2013) at CAPSS, Bose Institute, Kolkata, India, I have published one Phys. Rev. C paper ( Shear viscosity due to Landau damping from the quark-pion interaction,) and then from May, 2013 to April, 2015 as well as from October, 2015 to March, 2016 at UNESP, Sao Paulo, Brazil ( http://www.ift.unesp.br/en/ ), I have published the articles: Shear viscosity of a pion gas resulting from ρππ and σππ interactions,
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| Pion self-energy diagram for |
Interestingly we see that the πρ and πσ contributions play a complementary role in η to be non-divergent in the higher (T >0.100 GeV) and lower (T <0.100 GeV) temperature regions respectively. The lesson here is that consideration of both resonances in π−π scattering is strictly necessary to obtain a smooth, non divergent η for temperatures below the critical temperature,Tc≃0.175 GeV. See the figure below :
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| Upper : before folding & Lower : after folding by the spectral functions of rho and sigma mesons.. |
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| In the Quark matter quark (Q) may have quantum fluctuation of quark-pion loop, where pion is considered as pseudo scalar condensate. Similarly pion may also go through the quark-antiquark loop in the medium. |
In low temperature region, η is decreasing with increasing of T which is analogous to the behavior of liquid (From our daily life experience, we see that the cooking oil behaves like a less viscous medium when it is heated). Whereas in high temperature domain, η become an increasing function of T just like a system of gas.
