Speaker
Description
The field-theoretic renormalization group (RG) method was used to study the behavior of a randomly walking particle on a rough surface. The surface was given by the conserved Kardar--Parisi--Zhang (CKPZ) stochastic equation, and the random walk was governed by the standard diffusion equation for a particle in a uniform gravitational field. The complete model was presented as a field-theoretic model, which was found to be multiplicatively renormalizable and logarithmic for $ d = 2 $. The RG equation allowed us to identify stable fixed points corresponding to possible types of infrared (IR) asymptotic (long-time, large-distance) behavior. All critical dimensions were found exactly. In particular, the spreading law for the particle’s cloud was established, which differs from the standard expression $ R^2(t) \sim t $.
