Specific shear viscosity in hot rotating systems of paired fermions

The specific shear viscosity $\bar{\eta }$ of a classically rotating system of nucleons that interact via a monopole pairing interaction is calculated including the effects of thermal fluctuations and coupling to pair vibrations within the selfconsistent quasiparticle random-phase approximation. It is found that $\bar{\eta }$ increases with angular momentum $M$ at a given temperature $T$. In medium and heavy systems, $\bar{\eta }$ decreases with increasing $T$ at $T\ge$ 2 MeV and this feature is not affected much by angular momentum. But in lighter systems (with the mass number $A\le$ 20), $\bar{\eta }$ increases with $T$ at a value of $M$ close to the maximal value $M_{max}$, which is defined as the limiting angular momentum for each system. The values of $\bar{\eta }$ obtained within the schematic model as well as for systems with realistic single-particle energies are always larger than the universal lower-bound conjecture $\mathrm{\hslash }\mathrm{/}(4\pi k_B)$ up to $T$=5 MeV.