Shear and Bulk Viscosities of Hot Dense Matter

Shear and Bulk Viscosities of Hot Dense Matter Joe Kapusta University of Minnesota New Results from LHC and RHIC, INT, 25 May 2010

Is the matter created at RHIC a perfect fluid ? Physics Today, May 2010

Atomic and Molecular Systems In classical transport theory and so that as the density and/or cross section is reduced (dilute gas limit) the ratio gets larger. In a liquid the particles are strongly correlated. Momentum transport can be thought of as being carried by voids instead of by particles (Enskog) and the ratio gets larger.

Helium NIST data L. Csernai, L. Mc. Lerran and J. K.

Nitrogen NIST data L. Csernai, L. Mc. Lerran and J. K.

NIST data L. Csernai, L. Mc. Lerran and J. K.

2 D Yukawa Systems in the Liquid State Applications to dusty-plasmas and many other 2 D condensed matter systems. Liu & Goree (2005)

QCD • Chiral perturbation theory at low T (Prakash et al. ): grows with decreasing T. • Quark-gluon plasma at high T (Arnold, Moore, Yaffe): grows with increasing T.

QCD Low T (Prakash et al. ) using experimental data for 2 -body interactions. High T (Yaffe et al. ) using perturbative QCD. L. Csernai, L. Mc. Lerran and J. K.

Shear vs. Bulk Viscosity Shear viscosity is relevant for change in shape at constant volume. Bulk viscosity is relevant for change in volume at constant shape. Bulk viscosity is zero for point particles and for a radiation equation of state. It is generally small unless internal degrees of freedom (rotation, vibration) can easily be excited in collisions. But this is exactly the case for a resonance gas – expect bulk viscosity to be large near the critical temperature!

Lennard-Jones potential Meier, Laesecke, Kabelac J. Chem. Phys. (2005) Pressure fluctuations give peak in bulk viscosity.

QCD • Chiral perturbation theory at low T (Chen, Wang): grows with increasing T. • Quark-gluon plasma at high T (Arnold, Dogan, Moore, ): decreases with increasing T.

QCD Low T (Chen & Wang) using chiral perturbation theory. High T (Arnold et al. ) using perturbative QCD. ς/s rises dramatically as Tc is approached from above (Karsch, Kharzeev, Tuchin) Lattice w/o quarks (Meyer) → 0. 008 at T/Tc=1. 65 and 0. 065 at T/Tc=1. 24

QCD Low T (Prakash et al. ) using experimental data for 2 -body interactions. High T (Arnold et al. ) using perturbative QCD. ς/s rises dramatically as Tc is approached from above (Karsch, Kharzeev, Tuchin) Lattice w/o quarks (Meyer) → 0. 008 at T/Tc=1. 65 and 0. 065 at T/Tc=1. 24

Quasi-Particle Theory of Shear and Bulk Viscosity of Hadronic Matter • • • Relativistic Allows for an arbitrary number of hadron species Allows for arbitrary elastic and inelastic collisions Respects detailed balance Allows for temperature-dependent mean fields and quasi-particle masses • The viscosities and equation of state are consistent in the sense that the same interactions are used to compute them. P. Chakraborty & J. K.

Linear Sigma Model Calculated in the self-consistent Phi-derivable approximation = summation of daisy + superdaisy diagrams = mean field plus fluctuations P. Chakraborty & J. K.

Go beyond the mean field approximation by averaging over thermal fluctuations of the quasi-particles as indicated by the angular brackets. mean field fluctuation

Linear Sigma Model P. Chakraborty & J. K.

Linear Sigma Model Solution to the integral equation: P. Chakraborty & J. K.

Linear Sigma Model Relaxation time approximation P. Chakraborty & J. K.

Linear Sigma Model Increasing the vacuum sigma mass causes the crossover transition to look more like a second order transition. P. Chakraborty & J. K.

Linear Sigma Model P. Chakraborty & J. K. Violation of conformality

Linear Sigma Model P. Chakraborty & J. K. Violation of conformality

Romatschkes 2007 Both η/s and ζ/s depend on T – they are not constant. Beam energy scans at RHIC and LHC are necessary to infer their temperature dependence.

Conclusion • Hadron/quark-gluon matter should have a minimum in shear viscosity and a maximum in bulk viscosity at or near the critical or crossover point in the phase diagram analogous to atomic and molecular systems. • Sufficiently detailed calculations and experiments ought to allow us to infer the viscosity/entropy ratios. This are interesting dimensionless measures of dissipation relative to disorder.

Conclusion • RHIC and LHC are thermometers (hadron ratios, photon and lepton pair production) • RHIC and LHC are barometers (elliptic flow, transverse flow) • RHIC and LHC are viscometers (deviations from ideal fluid flow) • There is plenty of work for theorists and experimentalists!