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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.
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Submitted on : Monday, February 20, 2017 - 3:06:28 PM
Last modification on : Thursday, April 7, 2022 - 10:10:23 AM
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Frédéric Poitevin, Marc Delarue, Henri Orland. Beyond Poisson-Boltzmann: Numerical sampling of charge density fluctuations. 2016. ⟨cea-01472068⟩



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