Transport theory at the nanoscale. I. Surface waves

Small scale particle motion is the cause of dynamic roughening and plays a role during film growth. To study surface waves on the molecular level, a continuum approach is used that links atomic and macroscopic dynamics though a Fokker-Planck equation for the distribution of particle trajectories. The dynamic equation for the density interfacial profile includes inertia terms indispensable for high frequency fluctuations. For wave vectors below the critical value, an initial periodic deformation of the surface on the order of the density correlation length simply decays with time. Above the critical wave vector, collective periodic motion is induced in the interface. A picture of short lived, localized high frequency wavelets emerges with contributions from acoustic, capillary, and elastic surface modes.