Stochastic Escape In and Out of Equilibrium: Methods and Applications

这一建议是为了支持研究一大类随机过程的工作，这类随机过程既包括经典的也包括量子的，涉及噪声诱导的逃离吸引盆的局部稳定状态。拟议的研究包括开发新的数学技术来分析这些过程，并将它们应用于凝聚态物质和核物理中的各种公开问题，这些问题与系统在平衡点和远离平衡点的成核过程有关。本文所述研究项目的选择以三个目标为指导。它们是：开发技术，以扩大理论分析可获得的各种系统和情况；将这些技术应用于解决物理系统中的公开问题；以及对由此产生的预测进行实验和数值测试。整个研究计划的目标是在我们对受弱噪声干扰的非线性动力系统的理解方面取得重大进展，弱噪声是一类跨越许多科学学科的系统。由PI和合作者开发的数学方法将应用于广泛的系统，这些系统放在一起，在各种科学领域具有基本的科学重要性，同时具有前景广阔的未来技术应用。这些包括纳米磁体中的磁化反转、单价金属纳米线的稳定性和寿命、高角动量超形变核态的衰变、热激活-量子隧穿转变以及液晶中电对流图案的形成。这些问题可以通过PI和合作者的工作产生的统一的数学方法来解决。将为来自不同背景的博士后研究人员、研究生和本科生提供培训。例如，该提案包括在亚微米级铁磁环空中进行热致磁化反转研究的实验/数值/理论合作。这个实验已经处于初始阶段，旨在验证PI和其他人的理论预测，主要是由攻读博士论文的学生进行的。还应开展几项外展活动，包括在当地K-12学校的班级上做报告，为参加奖学金科学竞赛的纽约市高中生提供科学项目，以及在多学科暑期学校为其他领域的研究生讲课。最后，皮？S的工作对具有潜在技术重要性的领域的适用性已经导致了一项专利申请，并可能导致更多的专利申请。国家科学基础日记说明Proposal：0651077 Pi姓名：Stein，Daniel Printed

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