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Register a new userThe Shear Viscosity and Thermal Conductivity of Nuclear Pasta
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Added by
Charles J. Horowitz
Publication date
2008
fields
Physics
and research's language is
English
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We calculate the shear viscosity $eta$ and thermal conductivity $kappa$ of a nuclear pasta phase in neutron star crusts. This involves complex non-spherical shapes. We use semiclassical molecular dynamics simulations involving 40,000 to 100,000 nucleons. The viscosity $eta$ can be simply expressed in terms of the height $Z^*$ and width $Delta q$ of the peak in the static structure factor $S_p(q)$. We find that $eta$ increases somewhat, compared to a lower density phase involving spherical nuclei, because $Z^*$ decreases from form factor and ion screening effects. However, we do not find a dramatic increase in $eta$ from non-spherical shapes, as may occur in conventional complex fluids.
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We have explored the shear viscosity and electrical conductivity calculations for bosonic and fermionic medium, which goes from without to with magnetic field picture and then their simplified massless expressions. In presence of magnetic field, 5 independent velocity gradient tensors can be designed, so their corresponding proportional coefficients, connected with the viscous stress tensor provide us 5 shear viscosity coefficients. In existing litterateurs, two sets of tensors are available. Starting from them, present work has obtained two sets of expressions for 5 shear viscosity coefficients, which can be ultimately classified into three basic components: parallel, perpendicular and Hall components as one get same for electrical conductivity at finite magnetic field. Our calculations are based on kinetic theory approach in relaxation time approximation. Repeating same mathematical steps for finite magnetic field picture, which traditionally practiced for without field case, we have obtained 2 sets of 5 shear viscosity components, whose final expressions are in well agreements with earlier references, although a difference in methodology or steps can be clearly noticed. Realizing the massless results of viscosity and conductivity for Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein distribution function, we have applied them for massless quark gluon plasma and hadronic matter phases, which can provide us a rough order of strength, within which actual results will vary during quark-hadron phase transition. Present work also indicates that magnetic field might have some role for building perfect fluid nature in RHIC or LHC matter. The lower bound expectation of shear viscosity to entropy density ratio is also discussed.
Shear viscosity $eta$ is calculated for the nuclear matter described as a system of interacting nucleons with the van der Waals (VDW) equation of state. The Boltzmann-Vlasov kinetic equation is solved in terms of the plane waves of the collective overdamped motion. In the frequent-collision regime, the shear viscosity depends on the particle-number density $n$ through the mean-field parameter $a$, which describes attractive forces in the VDW equation. In the temperature region $T=15 - 40$~MeV, a ratio of the shear viscosity to the entropy density $s$ is smaller than 1 at the nucleon number density $n =(0.5 - 1.5),n^{}_0$, where $n^{}_0=0.16,$fm$^{-3}$ is the particle density of equilibrium nuclear matter at zero temperature. A minimum of the $eta/s$ ratio takes place somewhere in a vicinity of the critical point of the VDW system. Large values of $eta/sgg 1$ are, however, found in both the low-density, $nll n^{}_0$, and high-density, $n>2n^{}_0$, regions. This makes the ideal hydrodynamic approach inapplicable for these densities.
We compute the shear viscosity of QCD with matter, including almost all next-to-leading order corrections -- that is, corrections suppressed by one power of $g$ relative to leading order. We argue that the still missing terms are small. The next-to-leading order corrections are large and bring $eta/s$ down by more than a factor of 3 at physically relevant couplings. The perturbative expansion is problematic even at $T simeq 100$ GeV. The largest next-to-leading order correction to $eta/s$ arises from modifications to the qhat parameter, which determines the rate of transverse momentum diffusion. We also explore quark number diffusion, and shear viscosity in pure-glue QCD and in QED.
The shear viscosity of hot nuclear matter is investigated by using the mean free path method within the framework of IQMD model. Finite size nuclear sources at different density and temperature are initialized based on the Fermi-Dirac distribution. The results show that shear viscosity to entropy density ratio decreases with the increase of temperature and tends toward a constant value for $rhosimrho_0$, which is consistent with the previous studies on nuclear matter formed during heavy-ion collisions. At $rhosimfrac{1}{2}rho_0$, a minimum of $eta/s$ is seen at around $T=10$ MeV and a maximum of the multiplicity of intermediate mass fragment ($M_{text{IMF}}$) is also observed at the same temperature which is an indication of the liquid-gas phase transition.
The fireball concept of Rolf Hagedorn, developed in the 1960s, is an alternative description of hadronic matter. Using a recently derived mass spectrum, we use the transport model GiBUU to calculate the shear viscosity of a gas of such Hagedorn states, applying the Green-Kubo method to Monte-Carlo calculations. Since the entropy density is rising ad infinitum near $T_H$, this leads to a very low shear viscosity to entropy density ratio near $T_H$. Further, by comparing our results with analytic expressions, we find a nice extrapolation behavior, indicating that a gas of Hagedorn states comes close or even below the boundary $1/4pi$ from AdS-CFT.
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