1 / 19

Bulk viscosity of interacting Hadrons

Anton Wiranata and Madappa Prakash Department of Physics and Astronomy Ohio University, Athens, OH. Bulk viscosity of interacting Hadrons. Quark Matter 2009, March 30 – April 4, Knoxville, TN. Topics. Overview of results Bulk viscosity in the Chapman– Enskog approximation

elaina
Download Presentation

Bulk viscosity of interacting Hadrons

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Anton Wiranata and Madappa Prakash Department of Physics and Astronomy Ohio University, Athens, OH Bulk viscosity of interacting Hadrons Quark Matter 2009, March 30 – April 4, Knoxville, TN

  2. Topics • Overview of results • Bulk viscosity in the Chapman–Enskog approximation • Bulk viscosity and speed of sound • Analysis in limiting situations • Numerical results of ηv and ηv /s • Chiralpions • Massive interacting pions • Multi-component mixtures • Binary and N-species systems • Ongoing work and future plans Quark Matter 2009, March 30 – April 4, Knoxville, TN

  3. Bulk viscosity / entropy density vs T P.Arnold, et.al JHEP05, 051(2003) Kharzeev & Tuchin JHEP09, 093(2008) Chen and Wang, Arxiv:0711.4824v1 Wiranata & Prakash. Kapusta, arxiv:0809.3746v2 Quark Matter 2009, March 30 – April 4, Knoxville, TN

  4. Chapman-Enskog Approximation “For small deviations from equilibrium, the distribution function can be expressed in terms of hydrodynamic variables ( f(x,p) μ(x), u(x), T(x) ) and their gradients. Transport coefficients (viscosities, thermal conductivity, etc. ) are then calculable from relativistic kinetic theory.” φ(1) : Deviation function Equilibrium distribution function μ(x) : Chemical potential u(x) : Flow velocity T(x) : Temperature Quark Matter 2009, March 30 – April 4, Knoxville, TN

  5. Beginning with the relativistic Boltzman equation and inserting f(0) the solution (deviation function) has the general structure Quark Matter 2009, March 30 – April 4, Knoxville, TN

  6. Bulk Viscosity Ratio of specific heats First approximation : Reduced enthalpy : (ε + P) / nmc2 Relativistic Omega Integrals Relative momentum weight Thermal weight Transport cross section Relative momentum : g = mc sinh ψ Total momentum : P = 2mc cosh ψ Quark Matter 2009, March 30 – April 4, Knoxville, TN

  7. Bulk Viscosity & the Speed of Sound Chapman-Enskog 1st approximation Features thermodynamic variables The omega integral contains transport cross-section Utilizing Quark Matter 2009, March 30 – April 4, Knoxville, TN

  8. Analysis for limiting cases Nearly massless particles or very high temperatures (z << 1) : Massive particles such that z >> 1 : Lesson : For a given T, intermediate mass particles contribute significantly to ηv Quark Matter 2009, March 30 – April 4, Knoxville, TN

  9. Variational approximation Sean Gavin, Nucl. Phy. A 435, 826 (1985) Gavin’s result can be rewritten as Kapusta , arxiv:0809.3746v2 A similar analysis leads to the result that intermediate mass particles control the magnitude of ηv Quark Matter 2009, March 30 – April 4, Knoxville, TN

  10. Numerical results (interacting pions) Parametrization from Bertsch et al. , PR D37 (1988) 1202. Quark Matter 2009, March 30 – April 4, Knoxville, TN

  11. Entropy Density Non-interacting part Entropy Density Fugacity β =1/kT : Inverse Temperature Energy Density Pressure ``Venugopalan & Prakash   Nucl. Phys. A546 (1992) 718'' Interacting part (up to 2nd virial expansion) Kinematic Factor Thermal weight Interactions Quark Matter 2009, March 30 – April 4, Knoxville, TN

  12. Results (Interacting Pions) Prakash et al. , Phys. Rep. 227 (1993) 321 Bulk &Shear Viscosity Entropy Density ηv 3rd appro x 103 2nd 1st Total [GeV][fm-2][c-1] [fm-3] Non-interacting ηs 1st appro Interacting 2nd T[MeV] T[MeV] Quark Matter 2009, March 30 – April 4, Knoxville, TN

  13. Bulk viscosity / entropy density Chen and Wang, Arxiv:0711.4824v1 Wiranata & Prakash QGP sum rule Massless pions Lattice For chiral pions ηv/s increases with T in contrast to ηv /s for massive interacting pions Quark Matter 2009, March 30 – April 4, Knoxville, TN

  14. Multi-Component system Begin with binary mixture Ratio of specific heats Relative momentum weight Thermal weight Transport cross section W.A. Leeuwen, et.al Quark Matter 2009, March 30 – April 4, Knoxville, TN

  15. Binary mixture Results for constant cross-sections Quark Matter 2009, March 30 – April 4, Knoxville, TN

  16. Multi-component system Result for N – species at pth order of approximation Omega integral Coefficients to be determined Solubility conditions (assures 4-momentum conservation in collisions) Involves ratios of specific heats Quark Matter 2009, March 30 – April 4, Knoxville, TN

  17. 1st order calculation Coefficients to be determined Quark Matter 2009, March 30 – April 4, Knoxville, TN

  18. Ongoing work and future plans • Calculation of ηv & ηv /s for a mixture of interacting hadrons with masses up to 2 GeV. • Development of an approach to calculate the needed differentialcross-sections for hadron-hadron interactions including resonances up to 2 GeV. • Comparison of the Chapman-Enskog results with those of the Green-Kubo approach. • Inclusion of decay processes. • All the above for shear viscosity ηv and ηv /s Quark Matter 2009, March 30 – April 4, Knoxville, TN

  19. Thank you Quark Matter 2009, March 30 – April 4, Knoxville, TN

More Related