Speaker
Description
The talk is devoted to the model of random walk on a fluctuating rough surface using the field-theoretic renormalization group (RG). The surface is modelled by the well-known Kardar-Parisi-Zhang (KPZ) stochastic equation while the random walk is described by the standard diffusion equation for a particle in a uniform gravitational field. In the RG approach, possible types of infrared (IR) asymptotic (long-time, large-distance) behaviour are determined by IR attractive fixed points. Within the one-loop RG calculation (the leading order in $\varepsilon=2-d$, $d$ being the spatial dimension), we found six possible fixed points or curves of points. Two of them can be IR attractive: the Gaussian point (free theory) and the nontrivial point where the KPZ surface is rough but its interaction with the random walk is irrelevant.
We also explored consequences of the presumed existence in the KPZ model of a non-perturbative strong-coupling fixed point. We found that it gives rise to an IR attractive fixed point in the full-scale model with the nontrivial spreading law $R(t)\sim t^{1/z}$, where the exponent $z$ can be inferred from the non-perturbative analysis of the KPZ model.
The talk is based on
N. V. Antonov, N. M. Gulitskiy, P. I. Kakin. A. S. Romanchuk "Random walk on a random surface: implications of non-perturbative concepts and dynamical emergence of Galilean symmetry" // J. Phys. A: Math. Theor. 58, 115001 (2025)
