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Studying Nonequilibrium Steady States with Quantum Chemistry Methods

用量子化学方法研究非平衡稳态

基本信息

批准号：
1954580
负责人：
David Limmer
金额：
$ 33.56万
依托单位：
University of California-Berkeley
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-04-01 至 2024-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1954580&HistoricalAwards=false
关键词：
Studying Nonequilibrium Steady States Quantum

项目摘要

David Limmer of the University of California, Berkeley is supported by an award from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry to develop computational tools to study molecular systems driven far away from equilibrium. Such nonequilibrium conditions occur throughout the natural and synthetic world. Materials are seldom assembled quasi-statically. Chemical reactions are often initiated with excitation. Life would cease if not constantly supplied with sources of energy. Despite this ubiquity, there are few numerical tools designed to glean macroscopic consequences from these driven molecular components. Without such tools, progress in chemistry is stifled. There are few physical principles to act a guide, to bound possibilities, to explain observations and to predict novel behavior. By using recent developments in an area of mathematics known as large deviation theory, Dr. Limmer and his research group develop methods to fill this void. This allows them to address contemporary questions in active, driven, fluctuating, and flowing systems. These developments are done in conjunction with an effort to enhance scientific literacy through youth based scientific computing initiatives including games-based learning programs designed to convey basic nonequilibrium concepts. In order to develop novel numerical tools for studying driven molecular systems, Prof. Limmer and his research group use results from large deviation theory. Large deviation theory clarifies an isomorphism between algorithms to study nonequilibrium systems and those employed in traditional quantum chemistry, by defining an eigenvalue equation whose solution codifies the stability and response properties of general nonequilibrium steady states. While solving this equation exactly for interacting systems is exponentially hard, Dr. Limmer develops techniques for approximating it formally and estimating it stochastically. These techniques take inspiration from methods developed for solving the Schrödinger equation, including using diffusion and variation Monte Carlo, tensor products and many body theories. The class of algorithms Dr. Limmer develops represents a fundamentally different way to approach the simulation of driven molecular systems on a computer, which are predominately simulated by direct integration of an evolution equation. These techniques allow Dr. Limmer and his group to bridge the timescales available to simulation of nonequilibrium systems to those relevant to experiment, by targeting rare fluctuations. These techniques will be used to test the validity of basic constituent relationships of macroscopic transport for describing flows on nanoscales and for determining phase diagrams of active matter where traditional free energy based methods do not apply.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

加州大学伯克利分校的David Limmer得到了化学部化学理论、模型和计算方法计划的支持，该计划开发计算工具来研究远离平衡的分子系统。这种非平衡状态在整个自然界和人造世界中都存在。材料很少是准静态组装的。化学反应通常是在激发下开始的。如果没有源源不断的能量供应，生命就会停止。尽管无处不在，但很少有数值工具设计来收集这些受驱动的分子成分的宏观后果。如果没有这样的工具，化学方面的进步就会被扼杀。很少有物理原理来充当向导、限制可能性、解释观察和预测新的行为。通过利用被称为大偏差理论的数学领域的最新进展，利默博士和他的研究小组开发出了填补这一空白的方法。这使他们能够在活跃的、受驱动的、波动的和流动的系统中解决当代问题。这些发展是与通过以青年为基础的科学计算倡议，包括旨在传达基本非平衡概念的基于游戏的学习方案，来提高科学素养的努力相结合的。为了开发研究驱动分子系统的新的数值工具，Limmer教授和他的研究小组使用了大偏差理论的结果。大偏差理论通过定义一个本征值方程，阐明了研究非平衡系统的算法与传统量子化学中使用的算法之间的同构，该方程的解编码了一般非平衡稳态的稳定性和响应特性。虽然精确地求解相互作用系统的这个方程是非常困难的，但利默博士开发了形式上近似它并随机估计它的技术。这些技术的灵感来自于为求解薛定谔方程而开发的方法，包括使用扩散和变分蒙特卡罗、张量积和许多物体理论。利默博士开发的这类算法代表了一种完全不同的方式，可以在计算机上模拟受驱动的分子系统，这些系统主要是通过直接积分演化方程来模拟的。这些技术使利默博士和他的团队能够通过瞄准罕见的波动，将可用于模拟非平衡系统的时间尺度与那些与实验相关的时间尺度联系起来。这些技术将被用来测试宏观输运的基本组成关系的有效性，用于描述纳米尺度上的流动，并用于确定基于传统自由能方法不适用的活性物质的相图。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。