Quantum Bound of the Shear Viscosity of a Strongly Coupled Plasma

String theory methods led to the hypothesis that the ratio of a shear viscosity coefficient to the volume density of entropy of any physical system has a lower bound. Systems with strong coupling have a small viscosity as compared to weakly coupled plasmas in which the viscosity is proportional to the mean free path. Here, we have estimated the fully ionized strongly coupled plasma viscosity based on the dynamic experimental data on electrical conductivity and have shown that the ratio of viscosity to entropy of the strongly coupled plasma is very close to that of the lower bound predicted by the string theory.

Figure 1

Dependence of the ratio of shear viscosity coefficient to the volume density of entropy on coupling parameter. Calculations: 1, 2 present work at $T={10}^4\mathrm{K}$ with $r_M=r_D$ and $r_M\approx n^{-1/3}$ correspondently; 3-OCP model [11] at $T={10}^4\mathrm{K}$, 4-lowest level of OCP viscosity [11]. Experiments: open pentagon-xenon [20, 21], filled pentagon-xenon [28], open triangle-argon [20], semi top filled hexagon-argon [22], semi bottom filled hexagon-argon [23], semi filled right sided triangle-krypton [24], semi filled circle-helium [29], semi filled left sided triangle-mixture ${\mathrm{H}}_2$ and He [31]. Hydrogen: bottom faced filled triangle- [25], filled square-[27], filled star-cylindrical compression [26], open circle-plane compression [26], open rhombus-[30].

Figure 2

Comparison of different fluids with each other. Temperature dependence. Figure from Ref. 13 in logarithmic scale. Data from 13: filled circle-${\mathrm{H}}_2\mathrm{O}$, filled square-${\mathrm{N}}_2$, filled rhombus-He, filled hexagon-relativistic heavy ion collider, open bottom faced triangle-meson gas, open top faced triangle-quark gluon plasma, open hexagon-intermediate-energy collisions; filled pentagon-quark gluon plasma [15]; filled star-strongly coupled plasma, present work.