Studying Nonequilibrium Steady States with Quantum Chemistry Methods

加州大学伯克利分校的David Limmer获得了化学系化学理论、模型和计算方法项目的奖励，他开发了计算工具来研究远离平衡的分子系统。这种非平衡状态在自然界和合成世界中随处可见。材料很少以准静态方式组装。化学反应常由激发引起。如果没有源源不断的能源供应，生命就会停止。尽管这种现象无处不在，但很少有数值工具被设计用来从这些驱动的分子成分中收集宏观结果。没有这样的工具，化学的进步就会受到抑制。很少有物理原理可以作为指导，限定可能性，解释观察和预测新的行为。利默博士和他的研究小组利用被称为大偏差理论的数学领域的最新发展，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。这些发展与通过以青少年为基础的科学计算计划（包括旨在传达基本非平衡概念的基于游戏的学习计划）来提高科学素养的努力相结合。为了开发新的数值工具来研究驱动分子系统，Limmer教授和他的研究小组使用了大偏差理论的结果。通过定义一个特征值方程，大偏差理论澄清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性，该方程的解记录了一般非平衡稳态的稳定性和响应特性。虽然精确地为相互作用的系统求解这个方程是非常困难的，但利默博士开发了一种技术，可以正式地近似它，并随机地估计它。这些技术的灵感来自于解决Schrödinger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博士开发的算法代表了在计算机上模拟驱动分子系统的一种完全不同的方法，这种方法主要是通过直接整合进化方程来模拟的。这些技术使Limmer博士和他的团队能够通过瞄准罕见的波动，将模拟非平衡系统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输运的基本成分关系的有效性，以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。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.