Stochastic Escape In and Out of Equilibrium: Methods and Applications

这个奖项是为了研究一个广泛的随机过程，包括经典和量子，涉及噪声诱导的逃逸从局部稳定状态的吸引力盆。它还涉及到他们的应用程序在凝聚态物质（主要是在但不限于纳米级）与系统中的成核过程在平衡和远离各种开放的问题。有三个目标：技术的发展，扩大了各种系统和情况下访问的理论分析;这些技术的应用，以解决物理系统中的开放问题;和测试，实验和数值，所产生的预测。整个研究计划的目标是在我们对受弱噪声扰动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，并具有广阔的未来技术应用前景。这些包括磁化反转纳米磁体，稳定性和寿命的单价金属纳米线，状态之间的转换驱动的非线性系统，在扩展的系统中纳入非电位效应受到时空噪声，和电对流图案形成液晶。培训将提供给来自不同背景的研究生和本科生。还计划开展几项外联活动，包括为纽约市高中学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.