Stochastic Escape In and Out of Equilibrium: Methods and Applications

New York University, New York NY

Investigators

Abstract

This award is for the study of a broad class of stochastic processes, both classical and quantum, involving noise-induced escape from the basin of attraction of a locally stable state. It also involves their application to a variety of open problems in condensed matter (mostly at but not confined to the nanoscale) associated with nucleation processes in systems both at and away from equilibrium. There are three objectives: development of techniques that broaden the variety of systems and situations accessible to theoretical analysis; application of these techniques to the solution of open problems in physical systems; and testing, both experimentally and numerically, of the resulting predictions. The overall research program aims towards a significant advance in our understanding of nonlinear dynamical systems perturbed by weak noise, a class of systems that cuts across many scientific disciplines. Broader impacts: Mathematical methods developed by the PI and collaborators will be applied to a broad range of systems of fundamental scientific importance in a variety of scientific fields, and have promising future technological applications. These include magnetization reversal in nanomagnets, stability and lifetimes of monovalent metallic nanowires, transitions between states of driven nonlinear systems, incorporation of nonpotential effects in extended systems subject to spatiotemporal noise, and electroconvective pattern formation in liquid crystals. Training will be provided to graduate and undergraduate students from diverse backgrounds. Also planned are several outreach activities, including science projects for NYC high school students participating in science competitions for scholarships, and lectures to graduate students in other fields at multidisciplinary summer schools.