Electrical conductivity of an anisotropic quark gluon plasma: A quasiparticle approach

The study of transport coefficients of strongly interacting matter gained impetus after the discovery of the best fluid ever created in ultrarelativistic heavy-ion collision experiments. In this article, we have calculated one such coefficient, viz., electrical conductivity of the quark gluon plasma (QGP) phase, which exhibits an anisotropy in the momentum space. The relativistic Boltzmann's kinetic equation has been solved in the relaxation-time approximation to obtain the electrical conductivity. We have used the quasiparticle description to define the basic properties of QGP through the distribution functions of partons. We have compared our results with the corresponding results obtained in lattice as well as other model calculations. Further, we extend our model to calculate the electrical conductivity at finite chemical potential.

Figure 1

Variation of QPM and ideal distribution function with respect to momentum at two different temperatures. Solid and dash-dotted curves represent the light quark distribution function in QPM at $T=180$ and 500 MeV, respectively. Similarly short-dashed and long-dashed curves show the corresponding results in an ideal description.

Figure 2

Variation of QPM and ideal distribution functions with respect to temperature at two different momenta. Solid and dash-dotted curves represent the light quark distribution function in QPM at $p=0.01$ and 1000 MeV, respectively. Similarly short-dashed and long-dashed curves show the corresponding results in an ideal description.

Figure 3

Variations of ratios of electrical conductivity to temperature $\left({\sigma }_{\mathrm{el}}^{\mathrm{aniso}}/T\right)$ with respect to temperature at different values of anisotropy parameter $\xi =0,0.3$ and $0.6$, shown in the plot by solid, dashed, and dash-dotted lines, respectively. Solid circular gray points are the results as obtained from the dynamical quasiparticle model (DQPM) in Ref. [55]. All other symbols are the data points obtained from various lattice calculations [26, 27, 28, 29].

Figure 4

Variations of ratios of electrical conductivity to temperature $\left({\sigma }_{\mathrm{el}}^{\mathrm{aniso}}/T\right)$ with respect to temperature at two different values of anisotropy parameter $\xi =0$ and $0.6$ for quark chemical potential ${\mu }_q=0$ and ${\mu }_q=200\text{MeV}$.