April 14, 2023
Location: Utrecht University Campus, Minnaert, room 009
The KPZ problem and Statistics of Stochastic Flows
The KPZ (Kardar-Parisi-Zhang) problem is an extremely active research area which was actively studied in the last 15 years. In this talk we will discuss a geometrical approach to the problem of the KPZ Universality. Instead of looking at the height (interface) function and Airy processes, we will focus on the statistics of shocks and points of concentration of mass. We will also discuss the connection with the problem of the coalescing Brownian motions and coalescing fractional Brownian motions.
Homogeneous and not homogeneous nucleation in the three–state Blume–Capel model
We study the metastable behavior of the stochastic Blume–Capel model evolving according to the Glauber dynamics with zero boundary conditions. We will show that, due to the three–state character of the Blume–Capel model, the metastability scenario proven for periodic boundary condition changes deeply when different boundary conditions are considered.
The Hamiltonian of the Blume–Capel model depends on the magnetic field $h$ and the chemical potential $\lambda$. We study the heuristic in the whole region $\lambda,h > 0$, where the chemical potential term equally favors minus and plus spins with respect to zeroes and the magnetic field favors plusesand disadvantages minuses with respect to the zeroes, and we compere our results with the Blume-Capel model with periodic boundary conditions. Then, we analyze in detail the region $\lambda>h>0$. In this region, we identify the unique metastable state $\underline{-1}$, we compute the energy barrier from $\underline{-1}$ to the stable state $\underline{+1}$, and we find an estimate for the asymptotic behavior of the transition time from the metastable to the stable state as $\beta\to\infty$, where $\beta$ is the inverse of the temperature.