Critical wave vectors for transverse modes in strongly coupled dusty plasmas

Transverse collective modes of strongly coupled dusty plasmas are studied in the fluid phase. A memory function approach based on the generalized viscosity is employed to capture both the hydrodynamic limit and the second-moment sum rule. It is shown that shear modes do not exist at long wavelengths but do exist above a critical wave vector. Above the critical wave vector strong coupling gives rise to an incipient Brillouin structure in the dispersion. The emergence and damping of the shear mode is shown to depend on the generalized viscosity and a generalized relaxation time. Agreement with simulation data is shown to be excellent.