Beyond Poisson-Boltzmann: Numerical sampling of charge density fluctuations
Abstract
We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the mean-field solution given by the Poisson-Boltzmann equation, an original approach is proposed to numerically sample fluctuations around it, through the propagation of a Langevin like stochastic partial differential equation (SPDE). The diffusion tensor of the SPDE can be chosen so as to avoid the numerical complexity linked to long-range Coulomb interactions, effectively rendering the theory completely local. A finite-volume implementation of the SPDE is described, and the approach is illustrated with preliminary results on the study of a system made of two like-charge ions immersed in a bath of counter-ions.
Cite
@article{arxiv.1603.05892,
title = {Beyond Poisson-Boltzmann: Numerical sampling of charge density fluctuations},
author = {Frédéric Poitevin and Marc Delarue and Henri Orland},
journal= {arXiv preprint arXiv:1603.05892},
year = {2016}
}