Cutoff wave number for shear waves and Maxwell relaxation time in Yukawa liquids

Because liquids cannot resist shear except over very short distances comparable to the atomic spacing, shear sound waves (i.e., transverse phonons) propagate only for very short wavelengths. A measure of this limit is the cutoff wave number k(c), which is sometimes called the critical wave number. Previously k(c) was determined in molecular dynamics (MD) simulations by obtaining the dispersion relation. Another approach is developed in this paper by identifying the wave number at the onset of a negative peak in the transverse current correlation function. This method is demonstrated using a three-dimensional MD simulation of a Yukawa fluid, which mimics dusty plasmas. In general, k(c) is an indicator of conditions where elastic and dissipative effects are approximately balanced. Additionally, the crossover frequency for the real and imaginary terms of the complex viscosity of a dusty plasma is obtained; this crossover frequency corresponds to the Maxwell relaxation time.