W.N. Lacey Symposium in Chemical Engineering
In this presentation I will discuss two simple, but complex-valued integrals that enable the decoupling of many body problems in equilibrium statistical mechanics. These formulas allow partition functions in any ensemble to be transformed from traces over particle coordinates to functional integrals over continuous fields. The resulting statistical field theories are complex-valued, but nonetheless, embody the full microscopic details of the original particle models.
Such field theoretic descriptions have been known for more than 50 years, but with few exceptions, have enabled only approximate analytical calculations. Over the past decade, my 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 CS quantum field theory of cold bosons led us to conduct the first simulations of a model demonstrating superfluidity in cold He4.
This is part of the all day Lacey Symposium.