Effect of Coriolis force on the shear viscosity of quark matter: A nonrelativistic description

Shear viscosity becomes anisotropic in a rotating medium. It is discovered here that for rotating thermalized quantum systems such as those created in relativistic heavy-ion collisions, the coefficient of shear viscosity breaks up into five independent components. Similar phenomena were also discovered for quark-gluon plasma in the presence of the magnetic field. Like the Lorentz force at a finite magnetic field, the Coriolis force also creates anisotropic viscosity at nonzero rotation. As a first approach, for simplicity, the calculations are done in the nonrelativistic prescription, with a future proposal to extend it toward a relativistic description. Introducing the Coriolis force term in relaxation time approximated Boltzmann transport equation, we have found different effective relaxation times along the parallel, perpendicular, and Hall directions in terms of actual relaxation time and rotating time period. Comparing the present formalism with the finite magnetic field picture, we have shown the equivalence of roles between the rotating and cyclotron time periods, where the rotating time period is inverse of twice the angular velocity.

Figure 1

Schematic picture of rotating cylinder with fluid on the left side, whose one of the (cubical) fluid elements is zooming in the right side, where particles inside the fluid element box are randomly moving and facing Coriolis force.

Figure 2

Normalized parallel ($n=\parallel$), perpendicular ($n=\perp$), and Hall ($n=\times$) components of shear viscosity as well as shear viscosity without rotation are plotted against temperature.

Figure 3

Relative percentage of parallel ($n=\parallel$), perpendicular ($n=\perp$), Hall ($n=\times$) components of shear viscosity vs angular velocity.

Figure 4

Velocity gradients along XY, ZX, and ZY plane.

Figure 5

Velocity ($v$) vs momentum ($p$) relation for u quark, $\pi$ meson, and nucleons.