Studying Nonequilibrium Steady States with Quantum Chemistry Methods

加州大学伯克利分校的大卫·利默获得了化学系化学理论、模型和计算方法项目的一项奖励，以开发计算工具来研究远离平衡的分子系统。这样的非平衡状态发生在整个自然界和合成世界。材料很少准静态地组装。 化学反应通常由激发引发。 如果没有源源不断的能源供应，生命就会停止。尽管这种普遍性，有几个数值工具，旨在收集这些驱动分子组件的宏观后果。如果没有这些工具，化学的进步就会被扼杀。 很少有物理学原理可以作为指导，约束可能性，解释观察和预测新的行为。通过利用数学领域的最新发展，即大偏差理论，Limmer博士和他的研究小组开发了填补这一空白的方法。 这使他们能够在主动，驱动，波动和流动的系统中解决当代问题。这些发展是结合努力，以提高科学素养，通过青年为基础的科学计算举措，包括基于游戏的学习计划，旨在传达基本的非平衡概念。 为了开发用于研究驱动分子系统的新型数值工具，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，其解编码一般非平衡稳态的稳定性和响应特性，澄清了研究非平衡系统的算法与传统量子化学中所采用的算法之间的同构。虽然精确求解交互系统的这个方程是指数困难的，但Limmer博士开发了形式上近似和随机估计的技术。这些技术的灵感来自于解决薛定谔方程的方法，包括使用扩散和变分蒙特卡罗，张量积和许多体理论。Limmer博士开发的这类算法代表了在计算机上模拟驱动分子系统的一种根本不同的方法，这些系统主要是通过进化方程的直接积分来模拟的。这些技术使Limmer博士和他的团队能够通过瞄准罕见的波动，将非平衡系统模拟的时间尺度与实验相关的时间尺度联系起来。这些技术将用于测试宏观运输的基本组成关系的有效性，用于描述纳米尺度上的流动，并用于确定传统的基于自由能的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，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.