DYNAMICAL MODELS FOR SUPERDIFFUSION AND SUPERCONDUCTIVITY

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The proposal is devoted to mathematical models of statistical mechanics. Some of the most intriguing issues in modern research are the non-classical phenomena of superdiffusion and superconductivity and the newly discovered doubling effect for the second moment (representing the superdiffusion coefficient). The PI will investigate these phenomena by employing various chaotic dynamical systems -- periodic Lorentz gases, the Galton board, Bunimovich stadia, diamonds with cusps, etc. He will also study the classical gas of hard balls whose ergodicity remains to be proved in full generality. The proposal also includes multiparticle gases with a common thermostat and the fluid dynamics governed by Navier-Stokes equations and quasi-geostrophic equations.The proposal has a potentially broader impact on physics and other sciences. All its problems come from physics and the proposed research activities will have direct relevance to statistical mechanics, hydrodynamics, studies of electricity and superconductivity. The PI closely collaborates with physicists, other scientists, statisticians, and engineers. The PI publishes books and survey articles, maintains a web page with all his publications (including numerical data from computer experiments and the code), and uploads computer programs to MATLAB exchange public forums.