Transverse Density Fluctuations around the Ground State Distribution of Counterions near One Charged Plate: Stochastic Density Functional View

Abstract

We consider the Dean-Kawasaki (DK) equation of overdamped Brownian particles that forms the basis of the stochastic density functional theory. Recently, the linearized DK equation has successfully reproduced the full Onsager theory of symmetric electrolyte conductivity. In this paper, the linear DK equation is applied to investigate density fluctuations around the ground state distribution of strongly coupled counterions near a charged plate, focusing especially on the transverse dynamics along the plate surface. Consequently, we find a crossover scale above which the transverse density dynamics appears frozen and below which diffusive behavior of counterions can be observed on the charged plate. The linear DK equation provides a characteristic length of the dynamical crossover that is similar to the Wigner-Seitz radius used in equilibrium theory for the 2D one-component plasma, which is our main result. Incidentally, general representations of longitudinal dynamics vertical to the plate further suggest the existence of advective and electrically reverse flows; these effects remain to be quantitatively investigated.

Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling

“…This section is intended to provide a brief overview of theoretical approaches to jammed structures for explaining the relevance of stochastic DFT [44][45][46][47][48][49][50][51][52][53][54][55][56] to the degradation of hyperuniformity.…”

“…For assessing the applicability of density functional approaches to the free-energy landscape in glassy systems, let us compare stochastic DFT [44][45][46][47][48][49][50][51][52][53][54][55][56] and equilibrium DFT, or classical DFT conventionally used. [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74] Equilibrium DFT, [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74] one of the ensemble approaches, has been found relevant to investigate the free-energy landscape.…”

“…From stochastic DFT, [44][45][46][47][48][49][50][51][52][53][54][55][56] on the other hand, it is expected that the above-mentioned second scenario (i.e., (ii) stochastic and spatially correlated displacements) could be described in terms of stochastic density dynamics. To see this, a brief review of stochastic DFT is given below.…”

“…Of great practical use is the Dean-Kawasaki equation linearized with respect to density fluctuations around various reference density distributions. 44,[50][51][52][54][55][56] As seen below, stochastic DFT is formulated on the hybrid framework that combines equilibrium DFT and statistical field theory. 54,55,92 The hybrid framework allows us to investigate the metastable states considering fluctuations as clarified below.…”

“…To this end, we formulate an analytical form of the non-vanishing zero-wavevector structure factor that satisfies eqn (2) under the condition of eqn (7). A key ingredient of our formulation is the strongcoupling approximation of stochastic density functional theory (DFT) [44][45][46][47][48][49][50][51][52][53][54][55][56] which can consider intermittent fluctuations while fixing the density field at a given distribution of dense packings near and at jamming.…”