Viscosity, Shear Waves and Atomic Level Stress Correlations

The Green-Kubo equation relates the macroscopic stress-stress correlation function to a liquid's viscosity. The concept of the atomic level stresses allows the macroscopic stress-stress correlation function in the equation to be expressed in terms of the space/time correlations between the atomic level stress-stress correlation functions. Molecular dynamics studies show surprisingly long spatial extension of stress-stress correlations and also longitudinal and transverse waves propagating in liquids over ranges exceeding the system size. The results reveal that the range of propagation of shear waves corresponds to the range of distances relevant for viscosity. Thus our results show that viscosity is a fundamentally non-local quantity. We also show that periodic boundary conditions play very non-trivial, previously undiscussed, role in molecular dynamics simulations effectively masking the long range nature of viscosity.