Stochastic Escape In and Out of Equilibrium: Methods and Applications

该奖项是为了表彰对广泛的随机过程的研究，包括经典的和量子的，涉及从局部稳定状态的吸引力盆地中引起的噪声逃逸。它还涉及到它们在凝聚态物质（主要是但不限于纳米尺度）中与平衡和非平衡系统的成核过程相关的各种开放问题的应用。有三个目标：发展技术，扩大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；并从实验和数值两方面对结果预测进行检验。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。更广泛的影响：PI和合作者开发的数学方法将应用于各种科学领域中具有基础科学重要性的广泛系统，并具有良好的未来技术应用前景。这些包括纳米磁体的磁化反转，单价金属纳米线的稳定性和寿命，驱动非线性系统状态之间的转换，受时空噪声影响的扩展系统中的非势效应的结合，以及液晶中的电对流图案的形成。将为来自不同背景的研究生和本科生提供培训。还计划了几项外展活动，包括为纽约市高中生参加科学竞赛以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举办讲座。

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.