Stochastic Escape In and Out of Equilibrium: Methods and Applications

这一建议是为了支持研究一类广泛的随机过程，包括经典的和量子的，涉及从局部稳定状态的吸引盆地的噪声诱导逃逸。提出的研究包括发展新的数学技术来分析这些过程，并将其应用于凝聚态物质和核物理中与平衡和远离平衡的系统中的成核过程相关的各种开放问题。所提议活动的智力价值。以上所述的研究项目的选择以三个目标为指导。它们是：发展技术，拓宽理论分析的系统和情况的多样性；应用这些技术来解决物理系统中的开放问题；并对预测结果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，这是一类跨越许多科学学科的系统。拟议活动的更广泛影响。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础科学重要性，同时在未来具有很好的技术应用前景。这些研究包括纳米磁体的反磁化、单价金属纳米线的稳定性和寿命、高角动量超变形核态的衰变、量子隧道跃迁的热激活以及液晶中的电对流模式的形成。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访问。培训将提供给博士后研究人员，研究生，如果可能的话，来自不同背景的本科生。例如，该提案包括在亚微米尺度铁磁环空中热诱导磁化反转研究的实验/数值/理论合作。该实验已经处于初始阶段，旨在测试PI和其他人的理论预测，主要由研究生进行博士论文。还应该有一些推广活动，包括在当地K-12学校的课堂上做演讲，为纽约市高中生参加科学竞赛获得奖学金的科学项目，以及在多学科暑期学校为其他领域的研究生做讲座。最后，PI的适用性？美国在具有潜在技术重要性的领域的工作已经导致了一项专利申请，并且可能会导致更多。美国国家科学基金会期刊提案：0651077 PI姓名：Stein， danielprint

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