Studying Nonequilibrium Steady States with Quantum Chemistry Methods

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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.