A Finite-Volume Method for Fluctuating Dynamical Density Functional Theory

We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed scheme deals with general free-energy functionals, including, for instance, external fields or interaction potentials. This allows us to simulate a range of physical phenomena where thermal fluctuations play a crucial role, such as nucleation and other energy-barrier crossing transitions. A positivity-preserving algorithm for the density is derived based on a hybrid space discretization of the deterministic and the stochastic terms and different implicit and explicit time integrators. We show through numerous applications that not only our scheme is able to accurately reproduce the statistical properties (structure factor and correlations) of the physical system, but, because of the multiplicative noise, it allows us to simulate energy barrier crossing dynamics, which cannot be captured by mean-field approaches

Coherent States Formulation of Polymer Field Theory

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards' well known auxiliary-field (AF) framework, the CS formulation does not contain an embedded non-linear, non-local functional of the auxiliary fields, and the action of the field theory has a fully explicit, finite-order and semi-local polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.Comment: 14pages 8 figure

Renormalization of myoglobin-ligand binding energetics by quantum many-body effects

We carry out a first-principles atomistic study of the electronic mechanisms of ligand binding and discrimination in the myoglobin protein. Electronic correlation effects are taken into account using one of the most advanced methods currently available, namely a linear-scaling density functional theory (DFT) approach wherein the treatment of localized iron 3d electrons is further refined using dynamical mean-field theory (DMFT). This combination of methods explicitly accounts for dynamical and multi-reference quantum physics, such as valence and spin fluctuations, of the 3d electrons, whilst treating a significant proportion of the protein (more than 1000 atoms) with density functional theory. The computed electronic structure of the myoglobin complexes and the nature of the Fe-O2 bonding are validated against experimental spectroscopic observables. We elucidate and solve a long standing problem related to the quantum-mechanical description of the respiration process, namely that DFT calculations predict a strong imbalance between O2 and CO binding, favoring the latter to an unphysically large extent. We show that the explicit inclusion of many body-effects induced by the Hund's coupling mechanism results in the correct prediction of similar binding energies for oxy- and carbonmonoxymyoglobin.Comment: 7 pages, 5 figures. Accepted for publication in the Proceedings of the National Academy of Sciences of the United States of America (2014). For the published article see http://www.pnas.org/content/early/2014/04/09/1322966111.abstrac