School Seminar Program
Stochastic dynamics of interacting systems and asymmetric exclusion processes
Many complex systems of interacting particles behave on a phenomenological level in some random fashion. Examples come from areas as diverse as the growth of surfaces or the growth of biological systems, reaction-diffusion processes or the study of traffic flow. However, general theory for systems far from thermal equilibrium is still being developed. Hence one usually investigates specific model systems, hoping to gain insight into the general behavior of such systems. Numerical methods for simulation of stochastic dynamics range from Monte-Carlo to tensor networks.
However, there is an important class of so called asymmetric simple exclusion processes (ASEP) which allow analytic treatment. It is commonly accepted that different versions of ASEP provide an adequate description of statistical properties of one-dimensional diffusive and driven-diffusive systems. During the last decade the ASEP was a laboratory for obtaining the universal critical exponents and scaling functions for different universality classes.
My recent research was related to a study of the theory of critical phenomena in 2D statistical systems using advanced mathematical methods. In particular, I have obtained new powerful results in the representation theory of quantum groups. Surprisingly these results found applications in stochastic processes where they define the most general ASEP process with exactly solvable dynamics.
Dr. Vladimir Mangazeev graduated from the Moscow State University and obtained his PhD in Theoretical Physics from the Institute for High Energy Physics, Russia in 1993. In 1994 he moved to Australia to join the Department of Theoretical Physics as a Postdoctoral Fellow. In 1998 he relocated to the School of Mathematical Sciences, ANU as the Australian Research Council QEII Fellow to work on problems of quantum integrability in 3D. In 2004 he returned to the Department of Theoretical Physics. His current research topics include numerical renormalization group analysis of quantum interacting systems, integrable systems and quantum groups, applications to stochastic processes.