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.
This grant supported work to study a broad class of random processes, both classical and quantum, involving noise-induced escape from the basin of attraction of a locally stable state. The research resulted in the development of new mathematical techniques and their application to a variety of open problems in microscopically sized magnets and wires. The overall research program provided a significant advance in our understanding of nonlinear dynamical systems perturbed by weak noise, a class of systems that cuts across many scientific disciplines. Specific problems addressed included magnetization reversal in nanomagnets, stability and lifetimes of monovalent metallic nanowires, and more general questions regarding transitions between states of driven nonlinear systems. Our work has led to a series of theoretical advances in understanding how microscopic magnets switch their magnetization state under the influence of thermal noise or applied currents, which is important not only for fundamental physics reasons, but also because of the heavy use of these systems in information storage and processing. Work done under this and earlier grants have so far led to three patents. With regard to nanowires, the PI and his former graduate student, Lan Gong, developed during the current grant period a complete theory of noise-induced transtions in noncylindrical nanowires. This work has also led to a patent, and another patent based on this work is pending. Three graduate students were trained under this grant; two received their Ph.D.'s in the last three years, and one will receive a Ph.D. in December 2014.
