Formal methods for exactly converting both classical and quantum many body problems into molecularly-informed field theory models have been known for more than 50 years. These methods allow partition functions in any ensemble to be transformed from traces over particle coordinates to functional integrals over continuous fields. The resulting field theories are complex-valued and embody the full microscopic details and interactions of the original particle models. Until recently, such field-theoretic descriptions have enabled only approximate analytical studies of mostly homogeneous systems. Our group has shown that statistical field theory models of classical fluids, most notably polymers, can be directly tackled by numerical simulation. Such “field-theoretic simulations” (FTS) are advantaged over conventional particle-based computer simulations in a variety of situations, especially dense melts of high molecular weight polymers and systems subject to long-ranged interactions, such as polyelectrolytes. They are also well-suited for multi-scale simulations spanning length scales from nanometers to microns. This talk will introduce the construction of field theory models of polymeric fluids and the FTS framework. Two application examples will be provided: the design of uniquely hard-tough-elastic thermoplastics, and the phase behavior of oppositely charged polyelectrolytes. I will conclude by introducing a new “coherent states” (CS) representation of interacting polymers that offers potential computational advantages. A structural similarity with the quantum field theory of interacting bosons led us to conduct the first simulations of a CS model demonstrating superfluidity in cold 4He.

Field-theoretic simulations: From advanced materials to quantum liquids

255th National Meeting (2018)

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