arXiv subjects

Hiroshi Frusawa

Publications and source records attributed to Hiroshi Frusawa.

At least 19 recordsLinked to original sources

arXiv2025

Theoretical Basis for Classifying Hyperuniform States of Two-Component Systems

Hyperuniform states of matter exhibit unusual suppression of density fluctuations at large scales, contrasting sharply with typical disordered configurations. Various types of hyperuniformity emerge in multicomponent disordered systems, significantly enhancing their functional properties for advanced applications. This paper focuses on developing a theoretical framework for two-component hyperuniform systems. We provide a robust theoretical basis to identify novel conditions on structure factors for a variety of hyperuniform binary mixtures, classifying them into five distinct types with seven unique states. Our findings also offer valuable guidelines for designing multihyperuniform materials where each component preserves hyperuniformity, added to the overall hyperuniformity.

cond-mat.stat-mech↗

arXiv2024

Pole Analysis of the Inter-Replica Correlation Function in a Two-Replica System as a Binary Mixture: Mean Overlap in the Cluster Glass Phase

To investigate the cluster glass phase of ultrasoft particles, we examine an annealed two-replica system endowed with an attractive inter-replica field similar to that of a binary symmetric electrolyte. Leveraging this analogy, we conduct pole analysis on the total correlation functions in the two-replica system where the inter-replica field will eventually be switched off. By synthesizing discussions grounded in the pole analysis with a hierarchical view of the free-energy landscape, we derive an analytical form of the mean overlap between two replicas within the mean field approximation of the Gaussian core model. This formula elucidates novel numerical findings observed in the cluster glass phase.

cond-mat.stat-mech↗

arXiv2024

Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation

Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge--charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge--charge correlation function without the premise of anisotropic homogeneity in the electric field direction.

cond-mat.soft↗

arXiv2024

Replica Field Theory for a Generalized Franz--Parisi Potential of Inhomogeneous Glassy Systems: New Closure and the Associated Self-Consistent Equation

On approaching the dynamical transition temperature, supercooled liquids show heterogeneity over space and time. Static replica theory investigates the dynamical crossover in terms of the free energy landscape (FEL). Two kinds of static approaches have provided a self-consistent equation for determining this crossover, similar to the mode coupling theory for glassy dynamics. One uses the Morita-Hiroike formalism of the liquid state theory, whereas the other relies on the density functional theory (DFT). Each of the two approaches has advantages in terms of perturbative field theory. Here, we develop a replica field theory that has the benefits from both formulations. We introduce the generalized Franz-Parisi potential to formulate a correlation functional. Considering fluctuations around an inhomogeneous density determined by the Ramakrishnan--Yussouf DFT, we find a new closure as the stability condition of the correlation functional. The closure leads to the self-consistent equation involving the triplet direct correlation function. The present field theory further helps us study the FEL beyond the mean-field approximation.

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arXiv2022

Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis

We theoretically investigate an electric-field-driven system of charged spheres as a primitive model of concentrated electrolytes under an applied electric field. First, we provide a unified formulation for the stochastic charge and density dynamics of the electric-field-driven primitive model using the stochastic density functional theory (DFT). The stochastic DFT integrates various frameworks of the equilibrium and dynamic DFTs, the liquid state theory, and the field-theoretic approach, which allows us to justify in a unified manner various modifications previously made for the Poisson-Nernst-Planck model. Next, we consider stationary density-density and charge-charge correlation functions of the primitive model with a static electric field. We focus on an electric-field-induced synchronization between the emergence of density and charge oscillations, or the crossover from monotonic to oscillatory decay of density-density and charge-charge correlations. The correlation function analysis demonstrates the appearance of stripe states formed by segregation bands perpendicular to the external field. We also predict the following: (i) the electric-field-induced crossover occurs prior to the conventional Kirkwood crossover without an applied electric field, and (ii) the ion concentration dependence of the decay lengths at the electric-field-induced crossovers bears a similarity to the underscreening behavior found by simulation and theoretical studies on the oscillatory decay length in equilibrium.

cond-mat.soft↗

arXiv2021

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

Disordered and hyperuniform structures of densely packed spheres near and at jamming are characterized by vanishing of long-wavelength density fluctuations, or equivalently by long-range power-law decay of the direct correlation function (DCF). We focus on previous simulation results that exhibit degradation of hyperuniformity in jammed structures while maintaining the long-range nature of the DCF to a certain length scale. Here we demonstrate that a field-theoretic formulation of the stochastic density functional theory is relevant to explore the degradation mechanism. The strong-coupling expansion method of the stochastic density functional theory is developed to obtain the metastable chemical potential considering intermittent fluctuations in dense packings. The metastable chemical potential yields an analytical form of the metastable DCF that has a short-range cutoff inside the sphere while retaining the long-range power-law behavior. It is confirmed that the metastable DCF provides zero-wavevector limit of structure factor in quantitative agreement with the previous simulation results of degraded hyperuniformity. We can also predict the emergence of soft modes localized at the particle scale from plugging this metastable DCF into the linearized Dean-Kawasaki equation, a stochastic density functional equation.

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arXiv2021

On the equivalence of self-consistent equations for nonuniform liquids: a unified description of the various modifications

A variety of self-consistent (SC) equations have been proposed for non-uniform states of liquid particles under external fields, including adsorbed states at solid substrates and confined states in pores. External fields represent not only confining geometries but also fixed solutes. We consider SC equations ranging from the modified Poisson-Boltzmann equations for the Coulomb potential to the hydrostatic linear response equation for the equilibrium density distribution of Lennard-Jones fluids. Here, we present a unified equation that explains the apparent diversity of previous forms and proves the equivalence of various SC equations. This unified description of SC equations is obtained from a hybrid method combining the conventional density functional theory and statistical field theory. The Gaussian approximation of density fluctuations around a mean-field distribution is performed based on the developed hybrid framework, allowing us to derive a novel form of the grand-potential density functional that provides the unified SC equation for equilibrium density.

cond-mat.soft↗

arXiv2020

Free-energy functional of instantaneous correlation field in liquids: field-theoretic derivation of the closures

This paper presents a unified method for formulating a field-theoretic perturbation theory that encompasses the conventional liquid state theory. First, the free-energy functional of instantaneous correlation field is obtained from the functional-integral representation of the grand potential. Next, we demonstrate that the instantaneous free-energy functional yields a closure relation between the correlation functions in the mean-field approximation. Notably, the obtained closure relation covers a variety of approximate closures introduced in the liquid state theory.

cond-mat.stat-mech↗

arXiv2020

Ground-state correlation energy of counterions at a charged planar wall: Gibbs-Bogoliubov lower-bound approach

Recent simulation results imply the lowering of the ground-state correlation energy per counterion at a charged planar wall, compared with that of the 2D and 3D one-component plasma systems. Our aim is to correctly evaluate the ground-state energy of strongly-coupled counterion systems by considering a quasi-2D bound state where bound counterions are confined to a layer of molecular thickness. We use a variational approach based on the Gibbs-Bogoliubov inequality for the lower-bound free energy so that the liquid-state theory can be incorporated into the formulations. The soft mean spherical approximation demonstrates that the lowered ground-state energy can be reproduced by the obtained analytical form of a quasi-2D bound state.

cond-mat.soft↗

arXiv2020

Coarse-Grained Counterions in the Strong Coupling Limit

Recent Monte Carlo simulations (A. G. Moreira and R. R. Netz: Eur. Phys. J. E {\bf 8} (2002) 33) in the strong Coulomb coupling regime suggest strange counterion electrostatics unlike the Poisson-Boltzmann picture: when counterion-counterion repulsive interactions are much larger than counterion--macroion attraction, the coarse-grained counterion distribution around a macroion is determined only by the latter, and the former is irrelevant. Here, we offer an explanation for the apparently paradoxical electrostatics by mathematically manipulating the strong coupling limit.

cond-mat.soft↗

arXiv2020

Transverse density fluctuations around the ground state distribution of counterions near one charged plate: stochastic density functional view

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.

cond-mat.stat-mech↗

arXiv2020

Functional-integral approach to Coulomb fluids in the strong coupling limit

We have developed a field theory for strongly coupled Coulomb fluids, via introducing new functional--integral transformation of the electrostatic interaction energy. Our formalism not only reproduces the Lieb--Narnhofer lower bound, but also bridges logical gaps which previous approaches have involved.

cond-mat.stat-mech↗

arXiv2020

Electrostatic contribution to colloidal solvation in terms of the self-energy modified Boltzmann distribution

Electrostatic interactions make a large contribution to solvation free energy in ionic fluids such as electrolytes and colloidal dispersions. The electrostatic contribution to solvation free energy has been ascribed to the self-energy of a charged particle. Here we apply a variational field theory based on lower bound inequality to the inhomogeneous fluids of one-component charged hard-spheres, thereby verifying that the self-energy is given by the difference between the total correlation function and direct correlation function. Based on the knowledge of the liquid state theory, the self-energy specified in this study not only relates a direct correlation function to the Gaussian smearing of each charged sphere, but also provides the electrostatic contribution to solvation free energy that shows good agreement with simulation results. Furthermore, the Ornstein-Zernike equation leads to a new set of generalized Debye-Hückel equations reflecting the Gaussian distributed charges.

cond-mat.stat-mech↗

arXiv2018

Stochastic dynamics and thermodynamics around a metastable state based on the linear Dean-Kawasaki equation

The Dean-Kawasaki equation forms the basis of the stochastic density functional theory (DFT). Here it is demonstrated that the Dean-Kawasaki equation can be directly linearized in the first approximation of the driving force due to the free energy functional $F[ρ] $ of an instantaneous density distribution $ρ$, when we consider small density fluctuations around a metastable state whose density distribution $ρ^*$ is determined by the stationary equation $δF[ρ]/δρ|_{ρ=ρ^*}=μ$ with $μ$ denoting the chemical potential. Our main results regarding the linear Dean-Kawasaki equation are threefold. First, (i) the corresponding stochastic thermodynamics has been formulated, showing that the heat dissipated into the reservoir is negligible on average. Next, (ii) we have developed a field theoretic treatment combined with the equilibrium DFT, giving an approximate form of $F[ρ]$ that is related to the equilibrium free energy functional. Accordingly, (iii) the linear Dean-Kawasaki equation, which has been reduced to a tractable form expressed by the direct correlation function, allows us to compare the stochastic dynamics around metastable and equilibrium states, particularly in the Percus-Yevick hard sphere fluids; we have found that the metastable density is larger and the effective diffusion constant in the metastable state is smaller than the equilibrium ones in repulsive fluids.

cond-mat.stat-mech↗

arXiv2018

A variational principle behind van der Waals picture of strongly coupled plasmas

Various strong coupling theories of the one-component plasma have successfully predicted the thermodynamic and structural properties by separating the Coulomb potential into short- and long-ranged parts in {\itshape ad hoc} ways. Moreover, it has been demonstrated that the density-density correlation function in a mimic system with only the short-ranged interactions resembles that of the full Coulomb system, revealing that the van der Waals picture applies to the strongly coupled Coulomb systems. Here we provide a variational theory forming the basis of the van der Waals picture. Our approach provides hybrid formulations which combine both the liquid state theory and statistical field theory; essential use is made of the coarse-grained system with only long-raged part of Coulomb interactions as a reference system in introducing both lower bound variational principle and strong coupling expansion.

cond-mat.stat-mech↗

arXiv2018

Bridging the gap between correlation entropy functionals in the mean spherical and the hypernetted chain approximations: a field theoretic description

The correlation entropy as a functional of radial distribution function $g(r)$ (or the total correlation function $h(r)=g(r)-1$) in classical fluids has been obtained from the second Legendre transform of the grand potential. We focus on the correlation entropy difference between the two typical functionals in the mean spherical approximation (MSA) and the hypernetted chain (HNC) approximation. While the entropy functional difference between these approximations is of a simple form, the diagrammatic approaches in the liquid state theory are quite different from each other. Here we clarified the gap between the MSA and HNC functionals by developing a field theoretic description of the correlation functional theory that combines the variational principle of lower bound free energy, the conventional saddle-point approximation of a reference system to be optimized based on the variational principle, and the hybrid treatment of the saddle-point approximation and the fugacity expansion for modifying the primary optimization. Our formulation demonstrates that the MSA functional is reproduced by the first maximization of the variational functional in the saddle-point approximation, and that the HNC functional is obtained from the improved maximization of the virial term due to the fugacity expansion around the MSA functional. The virial term leads to the modification of a reference system interacting via the direct correlation function, thereby creating the correlation entropy difference.

cond-mat.stat-mech↗

arXiv2018

A self-consistent field theory of density correlations in classical fluids

More than half of a century has passed since the free energy of classical fluids defined by second Legendre transform was derived as a functional of density-density correlation function. It is now becoming an increasingly significant issue to develop the correlation functional theory that encompasses the liquid state theory, especially for glassy systems where out of equilibrium correlation fields are to be investigated. Here we have formulated a field theoretic perturbation theory that incorporates two-body fields (both of density-density correlation field and its dual field playing the role of two-body interaction potential) into a density functional integral representation of the Helmholtz free energy. Quadratic density fluctuations are only considered in the saddle-point approximation of two-body fields as well as density field. We have obtained a set of self-consistent field equations with respect to these fields, which simply reads a modified mean-field equation of density field where the bare interaction potential in the thermal energy unit is replaced by minus the direct correlation function given in the mean spherical approximation. Such replacement of the interaction potential in the mean-field equation belongs to the same category as the local molecular field theory proposed by Weeks and co-workers. Notably, it has been shown that even the mean-field part of the free energy functional given by the self-consistent field theory includes information on short-range correlations between fluid particles, similarly to the formulation of the local molecular field theory. The advantage of our field theoretic approach is not only that the modified mean-field equation can be improved systematically, but also that fluctuations of two-body fields in nonuniform fluids may be considered, which would be relevant especially for glass-forming liquids.

cond-mat.stat-mech↗

arXiv2015

A Non-stoichiometric Universality in Microbubble-Polyelectrolyte Complexation

We investigated the fundamental electrical properties of microbubbles (MBs) that are directly encapsulated by the addition of oppositely charged polyelectrolytes (PEs). Charge-reversal of the MB-PE complex particles has been observed by the microscopic electrophoresis method, revealing unusual overcharging behaviors in MB-PE complex solutions, as follows. The critical concentrations of cationic PEs added for overcharging were not only independent of their chain lengths and molecular species, but also much larger than stoichiometric neutralization points. Thus, we provide a theoretical sketch that considers the adsorption-desorption kinetics of small anions on the surface of genuine microbubbles, which can explain the inefficient charge-reversal.

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