Hiroshi Frusawa
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
The pressure in a classical Coulomb fluid at equilibrium is obtained from the Maxwell tensor at some point inside the fluid, by a suitable statistical average. For fluids in an Euclidean space, this is a fresh look on known results. But, for fluids in a curved space, a case which is of some interest, the unambiguous results from the Maxwell tensor approach have not been obtained by other methods.
Using the collective variables theory, we study the effect of competition between Coulomb and dispersion forces on the gas-liquid phase behaviour of a model ionic fluid, i.e. a charge-asymmetric primitive model with additional short-range attractive interactions. Both the critical parameters and the coexistence envelope are calculated in a one-loop approximation as a function of the parameter $α$ measuring the relative strength of the Coulomb to short-range interactions. We found the very narrow region of $α$ bounded from the both sides by tricritical points which separates the models with "no…
Statistical field theory of mechanical stresses in Coulomb fluids. Noether's theorem {\sl vs} General covariant approach
本文利用推广的诺特定理和广义协变方法，建立了非均匀库仑流体的统计场论，导出了含平均场与单圈涨落修正的应力张量，揭示了静电关联对局域应力的影响。
The structure factor for electric field correlations in the two dimensional Coulomb fluid is simulated and compared to theories of the dielectric function. Singular changes in the structure factor occur at the BKT insulator to conductor transition, as well as at a higher temperature correlation transition between a poor electrolyte and perturbed Debye-Hückel fluid. Structure factors are found to differ in the canonical and grand canonical ensembles, with the poor electrolyte showing full ensemble inequivalence. We identify mechanisms of `underscreening' and `pinch point' scattering that are re…
The classical (i.e. non-quantum) equilibrium statistical mechanics of a Coulomb fluid living on a pseudosphere (an infinite surface of constant negative curvature) is considered. The Coulomb fluid occupies a large disk communicating with a reservoir (grand-canonical ensemble). The total charge $Q$ on the disk fluctuates. In a macroscopic description, the charge correlations near the boundary circle can be described as correlations of a surface charge density $σ$. In a macroscopic approach, the variance of $Q$ and the correlation function of $σ$ are computed; they are universal. These macroscop…
A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact {\sl via} long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson-Boltzmann and Maier-Saupe equations. Explicit solutions are finally obtained for a rod-like counterion-only system in proximity of a charged planar wall, generalizing the standard Gouy-Chapman results. The nematic order parameter profile, the counter…
After a brief review of previous work, two exactly solvable two-dimensional models of a finite Coulomb fluid in a disc are studied. The charge correlation function near the boundary circle is computed. When the disc radius is large compared to the bulk correlation length, a correlation function of the surface charge density can be defined. It is checked, on the solvable models, that this correlation function does have the generic long-range behaviour, decaying as the inverse square distance, predicted by macroscopic electrostatics. In the case of a two-component plasma (Coulomb fluid made of t…
We present a personal view on the current state of statistical mechanics of Coulomb fluids with special emphasis on the interactions between macromolecular surfaces, concentrating on the weak and the strong coupling limits. Both are introduced for a (primitive) counterion-only system in the presence of macroscopic, uniformly charged boundaries, where they can be derived systematically. Later we show how this formalism can be generalized to the cases with additional characteristic length scales that introduce new coupling parameters into the problem. These cases most notably include asymmetric …
In a Coulomb fluid confined to a domain $V$, the dielectric susceptibility tensor $χ_V$ depends on the shape of $V$, even in the thermodynamic $V\to\infty$ limit. This paper deals with the classical two-dimensional one-component plasma formulated in an elliptic $V$-domain, equilibrium statistical mechanics is used. For the dimensionless coupling constant $Γ=$ even positive integer, the mapping of the plasma onto a discrete one-dimensional anticommuting-field theory provides a new sum rule. This sum rule confirms the limiting value of $χ_V$ predicted by macroscopic electrostatics and gives the …
Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, $h_λ({\bf r},{\bf r}')$, where $λ$ determines the interaction strength. To obtain $h_λ({\bf r},{\bf r}')$ we use the Ornstein-Zernike equation, and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. As the two equations do not form a closed set, an approximate closure relation is required and it determines a type of an approximation. In the present work we investigate the random phase approximation (RPA) closure. We determine th…
We will describe how logarithmic singularities arise as limits of Coulomb Gas integrals. Our approach will combine analytic properties of the time-like Liouville structure constants, together with the recursive formula of the Virasoro conformal blocks. Although the Coulomb Gas formalism forces a diagonal coupling between the chiral and antichiral sectors of the Conformal Field Theory (CFT), we present new results for the multi-screening integrals which are potentially interesting for applications to critical statistical systems described by Logarithmic CFTs. In particular our findings extend a…
The Coulomb gas partition sum is rewritten in terms of the path integrals formalism. It is shown that perturbation theories based on the Mayer expansion and on the path integrals method lead to the identical results. The well known Debye-Hukkel result for the case of 3D Coulomb plasma is completely rederived. An analogous result is obtained for the case of the Coulomb gas with dipoles. This result can be considered as a generalization of the Debye-Hukkel approximation. Other possible generalizations including the range of interaction potentials for which the Debye-Hukkel approximation can be a…
According to extensive experimental findings, the Ginzburg temperature $t_{G}$ for ionic fluids differs substantially from that of nonionic fluids [Schröer W., Weigärtner H. 2004 {\it Pure Appl. Chem.} {\bf 76} 19]. A theoretical investigation of this outcome is proposed here by a mean field analysis of the interplay of short and long range interactions on the value of $t_{G}$. We consider a quite general continuous charge-asymmetric model made of charged hard spheres with additional short-range interactions (without electrostatic interactions the model belongs to the same universality class a…
Using the collective variables method we revisit the estimates of the Ginzburg temperature for the Coulomb-dominated models of ionic fluids. We consider the charge-asymmetric primitive model supplemented by short-range attractive interactions in the vicinity of the gas-liquid critical point. For this model, we derive the effective Ising-like $ϕ^{4}$-model Hamiltonian expressed in terms of the collective variables describing the fluctuation modes of the total number density. We obtain the explicit expressions for all the Hamiltonian coefficients within the framework of the same approximation, n…
Variational field theory of macroscopic forces in Coulomb fluids
本研究基于变分场论与协变方法，将离子静电关联纳入总应力张量，建立并推导库仑流体在狭缝导电孔隙中的分离压力表达式。
In classical semi-infinite Coulomb fluids, two-point correlation functions exhibit a slow inverse-power law decay along a uniformly charged wall. In this work, we concentrate on the corresponding amplitude function which depends on the distances of the two points from the wall. Recently [L. Šamaj, J. Stat. Phys. {\bf 161}, 227 (2015)], applying a technique of anticommuting variables to a 2D system of charged rectilinear wall with "counter-ions only", we derived a relation between the amplitude function and the density profile which holds for any temperature. In this paper, using the Möbius con…
A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and particle numbers. A simple mean field approximation neglecting correlations yields a density profile which is monotonically decreasing with radius for all temperatures, in contrast to molecular dynamics simulations and experiments showing shell structure at lower temperatures. A more complete theoretical description including charge correlations is developed …
We propose a simplified version of local molecular field (LMF) theory to treat Coulomb interactions in simulations of ionic fluids. LMF theory relies on splitting the Coulomb potential into a short-ranged part that combines with other short-ranged core interactions and is simulated explicitly. The averaged effects of the remaining long-ranged part are taken into account through a self-consistently determined effective external field. The theory contains an adjustable length parameter sigma that specifies the cut-off distance for the short-ranged interaction. This can be chosen to minimize the …
The forging of strong correlations on decreasing temperature can take place without the arousal of conventional order. If this happens, as in some geometrically frustrated magnets, disorder can be a phenomenon more interesting than order itself. A Coulomb phase, for example, has critical-like pair-spin correlations, leading to neutron scattering \textit{pinch points} and emergent electromagnetism. Here we present a new instance of disorder in an Ising pyrochlore lattice: the \textit{Polarized Monopole Liquid} (PML), a dense monopole fluid with pinch points in the \textit{magnetic charge}-pair …
Thermodynamic potential of a neutral two-dimensional (2D) Cou\-lomb fluid, confined to a large domain with a smooth boundary, exhibits at any (inverse) temperature $β$ a logarithmic finite-size correction term whose universal prefactor depends only on the Euler number of the domain and the conformal anomaly number $c=-1$. A minimal free boson conformal field theory, which is equivalent to the 2D symmetric two-component plasma of elementary $\pm e$ charges at coupling constant $Γ=βe^2$, was studied in the past. It was shown that creating a non-neutrality by spreading out a charge $Q e$ at infin…
For a Coulomb system contained in a domain Λ, the dielectric susceptibility tensor χ_Λ is defined as relating the average polarization in the system to a constant applied electric field, in the linear limit. According to the phenomenological laws of macroscopic electrostatics, χ_Λ depends on the specific shape of the domain Λ. In this paper we derive, using the methods of equilibrium statistical mechanics in both canonical and grand-canonical ensembles, the shape dependence of χ_Λ and the corresponding finite-size corrections to the thermodynamic limit, for a class of general ν-dimensional (ν\…
The equilibrium density profiles in a classical multicomponent plasma near a hard wall made with a dielectric material characterized by a relative dielectric constant $\ew$ are studied from the first Born-Green-Yvon equation combined with Poisson equation in a regime where Coulomb coupling is weak inside the fluid. In order to prevent the collapse between charges with opposite signs or between each charge and its dielectric image inside the wall when $\ew >1$, hard-core repulsions are added to the Coulomb pair interaction. The charge-image interaction cannot be treated perturbatively and the d…
Using computer simulations and a thermodynamically self consistent integral equation we investigate the phase behaviour and thermodynamic anomalies of a fluid composed of spherical particles interacting via a two-scale ramp potential (a hard core plus a repulsive and an attractive ramp) and the corresponding purely repulsive model. Both simulation and integral equation results predict a liquid-liquid de-mixing when attractive forces are present, in addition to a gas-liquid transition. Furthermore, a fluid-solid transition emerges in the neighbourhood of the liquid-liquid transition region, lea…
The Debye-Hückel theory describes rigorously the thermal equilibrium of classical Coulomb fluids in the high-temperature $β\to 0$ regime ($β$ denotes the inverse temperature). It is generally believed that the Debye-Hückel theory and the systematic high-temperature expansion provide an adequate description also in the region of small {\em strictly positive} values of $β>0$. This hypothesis is tested in the present paper on a two-dimensional Coulomb gas of pointlike $+/-$ unit charges interacting via a logarithmic potential which is equivalent to an integrable sine-Gordon field model. In partic…
A study by W. R. Magro and D. M. Ceperley [Phys. Rev. Lett. {\bf 73}, 826 (1994)] has shown that the ground state of the two-dimensional fluid of charged bosons with logarithmic interactions is not Bose-condensed, but exhibits algebraic off-diagonal order in the single-particle density matrix $ρ(r)$. We use a hydrodynamic Hamiltonian expressed in terms of density and phase operators, in combination with an $f$-sum rule on the superfluid fraction, to reproduce these results and to extend the evaluation of the density matrix to finite temperature $T$. This approach allows us to treat the liquid …
In the framework of the grand-canonical ensemble of statistical mechanics, we give an exact diagrammatic representation of the density profiles in a classical multicomponent plasma near a dielectric wall. By a reorganization of Mayer diagrams for the fugacity expansions of the densities, we exhibit how the long-range of both the self-energy and pair interaction are exponentially screened at large distances from the wall. However, the self-energy due to Coulomb interaction with images still diverges in the vicinity of the dielectric wall and the variation of the density is drastically different…
We study the gas-liquid phase diagram and the crossover behavior of a simple model of ionic fluid: an equimolar binary mixture of equisized hard spheres interacting through screened Coulomb potentials which are repulsive between particles of the same species and attractive between particles of different species. Using our previous results, we obtain explicit expressions for the relevant coefficients of the effective $φ^{4}$ Ginzburg-Landau Hamiltonian in a one-loop approximation. Within the framework of this approximation, we calculate the critical parameters and gas-liquid coexistence curves …
Charge correlations in dense ionic fluids give rise to novel effects such as long-range screening and colloidal stabilization which are not predicted by the classic Debye-Huckel theory. We show that a Coulomb or charge-frustrated Ising model, which accounts for both long-range Coulomb and short-range molecular interactions, simply describes some of these ionic correlations. In particular, we obtain at mean field level and in simulations, a non-monotonic dependence of the screening length on the temperature. Using a combination of simulations and mean field theories, we study how the correlatio…
Systems of particles interacting through a screened Coulomb potential of the Debye-Yukawa form are considered. The pressure is obtained from the stress tensor of the field corresponding to the Yukawa interaction, by a suitable statistical average. This approach is especially appropriate for systems living in a curved space. In a curved space, a self contribution to the pressure appears, and it is essential to take it into account for retrieving a correct pressure when the Yukawa interaction tends to the Coulomb interaction.
A vibrational model of heat conduction in liquids with soft pairwise interactions is applied to estimate the thermal conductivity coefficient of strongly coupled Yukawa fluids. A reasonable agreement with the available data from numerical simulations is observed. The results can be useful in the context of strongly coupled plasma and complex (dusty) plasma fluids, when Yukawa (or screened Coulomb) interaction potential is applicable.
Equilibrium particle densities near a hard wall are studied for a quantum fluid made of point charges which interact via Coulomb potential without any regularization. In the framework of the grand-canonical ensemble, we use an equivalence with a classical system of loops with random shapes, based on the Feynman-Kac path-integral representation of the quantum Gibbs factor. After systematic resummations of Coulomb divergences in the Mayer fugacity expansions of loop densities, there appears a screened potential $ϕ$. It obeys an inhomogeneous Debye-Hückel equation with an effective screening leng…
The Stokes-Einstein (SE) relation between the self-diffusion and shear viscosity coefficients operates in sufficiently dense liquids not too far from the liquid-solid phase transition. By considering four simple model systems with very different pairwise interaction potentials (Lennard-Jones, Coulomb, Debye-Hückel or screened Coulomb, and the hard sphere limit) we identify where exactly on the respective phase diagrams the SE relation holds. It appears that the reduced excess entropy $s_{\rm ex}$ can be used as a suitable indicator of the validity of the SE relation. In all cases considered th…
The use of variational method in functional integral approach is discussed for fermion and boson systems with Coulomb interaction. The formal general expression of thermodynamic potential is obtained by Feynman path integral technique and representation of Coulomb interaction with functional integrals. Introduced additional complex field show to transform the problem to calculation of functional integrals containing third order vertices. The thermodynamic potential can be found from variational principle with respect to field cumulants. The calculation of the equation of state and critical pro…
In this brief review I will discuss criticality in strongly correlated fluids. Unlike simple fluids, molecules of which interact through short ranged isotropic potential, particles of strongly correlated fluids usually interact through long ranged forces of Coulomb or dipolar form. While for simple fluids mechanism of phase separation into liquid and gas was elucidated by van der Waals more than a century ago, the universality class of strongly correlated fluids, or in some cases even existence of liquid-gas phase separation remains uncertain.
We present an exact field theoretical representation of the statistical mechanics of classical hard-core Coulomb systems. This approach generalizes the usual sine-Gordon theory valid for point-like charges or lattice systems to continuous Coulomb fluids with additional short-range interactions. This formalism is applied to derive the equation of state of the restricted primitive model of electrolytes in the low fugacity regime up to order $ρ^{5/2}$ ($ρ$ number density). We recover the results obtained by Haga by means of Mayer graphs expansions.
Power spectrum of magnetic relaxation in spin ice: anomalous diffusion in a Coulomb fluid
针对自旋冰Dy₂Ti₂O₇磁化噪声功率谱S(f,T)高频尾部反常指数b(T)的文献矛盾，本研究通过高频（达10⁶ Hz）交流磁化率测量准确估计2-20 K的b(T)，发现之前测量低估该指数，确定其与b=2的偏差持续至20 K且具样品依赖性，完善了致密库仑流体单极扩散的动力学表征。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。