High-frequency elastic moduli of two-dimensional Yukawa fluids and solids

An approach to calculate high-frequency bulk and shear moduli of two-dimensional (2D) weakly screened Yukawa fluids and solids is presented. Elastic moduli are directly related to sound velocities and other important characteristics of the system. In this article, we discuss these relations and present an exemplary calculation of the longitudinal, transverse, and instantaneous sound velocities and derive a differential equation for the Einstein frequency. Simple analytical results presented demonstrate good accuracy when compared with numerical calculations. The obtained results can be particularly useful in the context of 2D colloidal and complex (dusty) plasma monolayers.