Stochastic Escape In and Out of Equilibrium: Methods and Applications

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This proposal is for the support of work to study a broad class of stochastic processes,both classical and quantum, involving noise-induced escape from the basin of attractionof a locally stable state. The proposed research involves the development of newmathematical techniques for analyzing these processes, and their application to avariety of open problems in condensed matter and nuclear physics associated withnucleation processes in systems both at and away from equilibrium.Intellectual merit of proposed activity. The choice of research projects described hereinis guided by three objectives. They are: development of techniques that broaden thevariety of systems and situations accessible to theoretical analysis; application of thesetechniques to the solution of open problems in physical systems; and testing, bothexperimentally and numerically, of the resulting predictions. The overall researchprogram aims towards a significant advance in our understanding of nonlineardynamical systems perturbed by weak noise, a class of systems that cuts across manyscientific disciplines.Broader impact of proposed activity. Mathematical methods developed by the PI andcollaborators will be applied to a broad range of systems that, put together, are offundamental scientific importance in a variety of scientific fields, and at the same timehave promising future technological applications. These include magnetization reversalin nanomagnets, stability and lifetimes of monovalent metallic nanowires, decay ofhigh-angular momentum superdeformed nuclear states, the thermal activation$quantumtunneling transition, and electroconvective pattern formation in liquid crystals. Theseproblems are accessible through a unified mathematical approach resulting from thework of PI and collaborators. Training will be provided to postdoctoral researchers,graduate students, and, if possible, undergraduate students from diverse backgrounds.For example, the proposal includes an experimental/numerical/theoretical collaborationin the study of thermally induced magnetization reversal in submicron-scaleferromagnetic annuli. The experiment, already in its initial stages, is designed to testtheoretical predictions of the PI and others, and is largely being carried out by agraduate student towards a Ph.D. thesis. There should also be several resultingoutreach activities, including presentations to classes at local K-12 schools, scienceprojects for NYC high school students participating in science competitions forscholarships, and lectures to graduate students in other fields at multidisciplinarysummer schools. Finally, the applicability of the PI?s work to areas of potentialtechnological importance has already led to one patent application, and is likely to leadto more.NATIONAL SCIENCE FOUNDATIONDiary NoteProposal:0651077 PI Name:Stein, DanielPrinted