Applied Mathematics Seminar

Date/Time/Room: Friday (11/16/2001) at 2:00 pm in 304 Pickard Hall

Speaker: H. Keith McDowell, Vice President for Research and Information Technology, Department of Chemistry and Biochemistry, University of Texas at Arlington

``Stochastic Electron Dynamics: A Challenge for some new Mathematics''

Abstract: Brownian motion and the associated Langevin stochastic differential equation have served for a century as the model or paradigm for noise driven motion or propagation. In this talk I present a quantum version of a noise driven process in which the dynamics of electrons coupled to a large reservoir of electrons that serves as a bath is modeled by a second-quantized, stochastic differential equation. The challenge of such a model is to maintain the Fermi-Dirac statistics of the electrons (also known as the Pauli Exclusion Principle). We introduce a novel random walk in which the sequence of steps of a random walker, or phase in quantum mechanical language, is preserved to allow for subsequent interference. Specific calculations on simple mechanical systems will be demonstrated.