arXiv subjects

Ladislav Samaj

Publications and source records attributed to Ladislav Samaj.

16 recordsLinked to original sources

arXiv2020

Strong-coupling theory of counterions with hard cores between symmetrically charged walls

By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis have focused on point-like counterions, we treat them as charged hard spheres. We thus work out the fate of like-charge attraction when steric effects are at work. The analytical approach partitions counterions in two sub-populations, one for each plate, and integrates out one sub-population to derive an effective Hamiltonian for the remaining one. The effective Hamiltonian features plaquette four-particle interactions, and it is worked out by computing a Gibbs-Bogoliubov inequality for the free energy. At the root of the treatment is the fact that under strong electrostatic coupling, the system of charges forms an ordered arrangement, that can be affected by steric interactions. Fluctuations around the reference positions are accounted for. To dominant order at high coupling, it is found that steric effects do not significantly affect the interplate effective pressure, apart at small distances where hard sphere overlap are unavoidable, and thus rule out configurations.

cond-mat.soft↗

arXiv2018

The asymmetric Wigner bilayer

We present a comprehensive discussion of the so-called asymmetric Wigner bilayer system, where mobile point charges, all of the same sign, are immersed into the space left between two parallel, homogeneously charged plates (with possibly different charge densities). At vanishing temperatures, the particles are expelled from the slab interior; they necessarily stick to one of the two plates, and form there ordered sublattices. Using complementary tools (analytic and numerical) we study systematically the self-assembly of the point charges into ordered ground state configurations as the inter-layer separation and the asymmetry in the charge densities are varied. The overwhelming plethora of emerging Wigner bilayer ground states can be understood in terms of the competition of two strategies of the system: the desire to guarantee net charge neutrality on each of the plates and the effort of the particles to self-organize into commensurate sublattices. The emerging structures range from simple, highly commensurate (and thus very stable) lattices (such as staggered structures, built up by simple motives) to structures with a complicated internal structure. The combined application of our two approaches (whose results agree within remarkable accuracy) allows to study on a quantitative level phenomena such as over- and underpopulation of the plates by the mobile particles, the nature of phase transitions between the emerging phases (which pertain to two different universality classes), and the physical laws that govern the long-range behaviour of the forces acting between the plates. Extensive Monte Carlo simulations, which have been carried out at small, but finite temperatures along selected, well-defined pathways in parameter space confirm the analytical and numerical predictions within high accuracy.

cond-mat.soft↗

arXiv2015

Poisson-Boltzmann thermodynamics of counter-ions confined by curved hard walls

We consider a set of identical mobile point-like charges (counter-ions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively 1D plates and the 2D cylinder have already been solved, the 3D sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion/explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counter-ions inside a charged sphere (salt-free system).

cond-mat.soft↗

arXiv2015

Phase diagram and critical properties of Yukawa bilayers

We study the ground-state Wigner bilayers of pointlike particles with Yukawa pairwise interactions, confined to the surface of two parallel hard walls at dimensionless distance $η$. The model involves as limiting cases the unscreened Coulomb potential and hard spheres. The phase diagram of Yukawa particles, studied numerically by Messina and Löwen [Phys. Rev. Lett. 91 (2003) 146101], exhibits five different staggered phases as $η$ varies from 0 to intermediate values. We present a lattice summation method using the generalized Misra functions which permits us to calculate the energy per particle of the phases with a precision much higher than usual in computer simulations. This allows us to address some tiny details of the phase diagram. Going from the hexagonal phase I to phase II is shown to occur at $η=0$, which resolves a longtime controversy. We find a tricritical point where Messina and Löwen suggested a coexistence domain of several phases which was suggested to divide the staggered rhombic phase into two separate regions. Our calculations reveal one continuous region for this rhombic phase with a very narrow connecting channel. Further we show that all second-order phase transitions are of mean-field type. We also derive the asymptotic shape of critical lines close to the Coulomb and hard-spheres limits. In and close to the hard-spheres limit, the dependence of the internal parameters of the present phases on $η$ is determined exactly.

cond-mat.soft↗

arXiv2013

Counter-ions at single charged wall: Sum rules

For inhomogeneous classical Coulomb fluids in thermal equilibrium, like the jellium or the two-component Coulomb gas, there exists a variety of exact sum rules which relate the particle one-body and two-body densities. The necessary condition for these sum rules is that the Coulomb fluid possesses good screening properties, i.e. the particle correlation functions or the averaged charge inhomogeneity, say close to a wall, exhibit a short-range (usually exponential) decay. In this work, we study equilibrium statistical mechanics of an electric double layer with counter-ions only, i.e. a globally neutral system of equally charged point-like particles in the vicinity of a plain hard wall carrying a fixed uniform surface charge density of opposite sign. At large distances from the wall, the one-body and two-body counter-ion densities go to zero slowly according to the inverse-power law. In spite of the absence of screening, all known sum rules are shown to hold for two exactly solvable cases of the present system: in the weak-coupling Poisson-Boltzmann limit (in any spatial dimension larger than one) and at a special free-fermion coupling constant in two dimensions. This fact indicates an extended validity of the sum rules and provides a consistency check for reasonable theoretical approaches.

cond-mat.soft↗

arXiv2013

Thermodynamics of two-component log-gases with alternating charges

We consider a one-dimensional gas of positive and negative unit charges interacting via a logarithmic potential, which is in thermal equilibrium at the (dimensionless) inverse temperature $β$. In a previous paper [Samaj, L.: J. Stat. Phys. 105, 173-191 (2001)], the exact thermodynamics of the unrestricted log-gas of pointlike charges was obtained using an equivalence with a (1+1)-dimensional boundary sine-Gordon model. The present aim is to extend the exact study of the thermodynamics to the log-gas on a line with alternating $\pm$ charges. The formula for the ordered grand partition function is obtained by using the exact results of the Thermodynamic Bethe ansatz. The complete thermodynamics of the ordered log-gas with pointlike charges is checked by a small-$β$ expansion and at the collapse point $β_c=1$. The inclusion of a small hard core around particles permits us to go beyond the collapse point. The differences between the unconstrained and ordered versions of the log-gas are pointed out.

cond-mat.stat-mech↗

arXiv2012

Long-range correlations of the surface charge density between electrical media with flat and spherical interfaces

We study the asymptotic long-range behavior of the time-dependent correlation function of the surface charge density induced on the interface between two media of distinct dielectric functions which are in thermal equilibrium with one another as well as with the radiated electromagnetic field. We start with a short review which summarizes the results obtained by using quantum and classical descriptions of media, in both non-retarded and retarded regimes of particle interactions. The classical static result for the flat interface is rederived by using a combination of the microscopic linear response theory and the macroscopic method of electrostatic image charges. The method is then applied to the case of a spherically shaped interface between media.

cond-mat.stat-mech↗

arXiv2011

Optimized t-expansion method for the Rabi Hamiltonian

A polemic arose recently about the applicability of the $t$-expansion method to the calculation of the ground state energy $E_0$ of the Rabi model. For specific choices of the trial function and very large number of involved connected moments, the $t$-expansion results are rather poor and exhibit considerable oscillations. In this letter, we formulate the $t$-expansion method for trial functions containing two free parameters which capture two exactly solvable limits of the Rabi Hamiltonian. At each order of the $t$-series, $E_0$ is assumed to be stationary with respect to the free parameters. A high accuracy of $E_0$ estimates is achieved for small numbers (5 or 6) of involved connected moments, the relative error being smaller than $10^{-4}$ (0.01%) within the whole parameter space of the Rabi Hamiltonian. A special symmetrization of the trial function enables us to calculate also the first excited energy $E_1$, with the relative error smaller than $10^{-2}$ (1%).

quant-ph↗

arXiv2011

High orders of Weyl series for the heat content

This article concerns the Weyl series of spectral functions associated with the Dirichlet Laplacian in a $d$-dimensional domain with a smooth boundary. In the case of the heat kernel, Berry and Howls predicted the asymptotic form of the Weyl series characterized by a set of parameters. Here, we concentrate on another spectral function, the (normalized) heat content. We show on several exactly solvable examples that, for even $d$, the same asymptotic formula is valid with different values of the parameters. The considered domains are $d$-dimensional balls and two limiting cases of the elliptic domain with eccentricity $ε$: A slightly deformed disk ($ε\to 0$) and an extremely prolonged ellipse ($ε\to 1$). These cases include 2D domains with circular symmetry and those with only one shortest periodic orbit for the classical billiard. We analyse also the heat content for the balls in odd dimensions $d$ for which the asymptotic form of the Weyl series changes significantly.

math.SP↗

arXiv2009

Fluctuations of Electromagnetic Field at the Interface Between Media

This work is about fluctuations of the surface charge between two media with distinct dielectric functions. The long-range correlation of the surface charge fluctuations is treated classically and quantum mechanically, in the non-retarded and retarded regimes.

cond-mat.stat-mech↗

arXiv2009

Charge and Current Sum Rules in Quantum Media Coupled to Radiation II

This paper is a continuation of the previous study [Šamaj, L.: J. Stat. Phys. {\bf 137}, 1-17 (2009)], where a sequence of sum rules for the equilibrium charge and current density correlation functions in an infinite (bulk) quantum media coupled to the radiation was derived by using Rytov's fluctuational electrodynamics. Here, we extend the previous results to inhomogeneous situations, in particular to the three-dimensional interface geometry of two joint semi-infinite media. The sum rules derived for the charge-charge density correlations represent a generalization of the previous ones, related to the interface dipole moment and to the long-ranged tail of the surface charge density correlation function along the interface of a conductor in contact with an inert (not fluctuating) dielectric wall, to two fluctuating semi-infinite media of any kind. The charge-current and current-current sum rules obtained here are, to our knowledge, new. The current-current sum rules indicate a breaking of the directional invariance of the diagonal current-current correlations by the interface. The sum rules are expressed explicitly in the classical high-temperature limit (the static case) and for the jellium model (the time-dependent case).

cond-mat.stat-mech↗

arXiv2009

Charge and Current Sum Rules in Quantum Media Coupled to Radiation

This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov's fluctuational electrodynamics. A technique is developed to extract the classical and purely quantum-mechanical parts of these sum rules. The sum rules are critically tested in the classical limit and on the jellium model. A comparison is made with microscopic approaches to systems of particles interacting through Coulomb forces only (the non-retarded regime). In contrast with microscopic results, the current-current correlation function is found to be integrable in space, in both classical and quantum regimes.

cond-mat.stat-mech↗

arXiv2009

Equilibrium long-ranged charge correlations at the surface of a conductor coupled to the electromagnetic radiation

This study is related to the fluctuation theory of electromagnetic fields, charges and currents. The three-dimensional system under consideration is a semi-infinite conductor, modeled by the jellium, in vacuum. In previous theoretical studies it was found that the correlation functions of the surface charge density on the conductor decay as the inverse cube of the distance at asymptotically large distances. The prefactor to this asymptotic decay was obtained in the classical limit and in the quantum case without retardation effects. To describe the retarded regime, we study a more general problem of the semi-infinite jellium in thermal equilibrium with the radiated electromagnetic field. By using Rytov's fluctuational electrodynamics we show that, for both static and time-dependent surface charge correlation functions, the inclusion of retardation effects causes the quantum prefactor to take its universal static classical form, for any temperature.

cond-mat.stat-mech↗

arXiv2009

Equilibrium long-ranged charge correlations at the interface between media coupled to the electromagnetic radiation

We continue studying long-ranged quantum correlations of surface charge densities on the interface between two media of distinct dielectric functions which are in thermal equilibrium with the radiated electromagnetic field. Two regimes are considered: the non-retarded one with the speed of light $c$ taken to be infinitely large and the retarded one with finite value of $c$. The analysis is based on results obtained by using fluctuational electrodynamics in [L. Šamaj and B. Jancovici, Phys. Rev. E {\bf 78}, 051119 (2008)]. Using an integration method in the complex plane and the general analytic properties of dielectric functions in the frequency upper half-plane, we derive explicit forms of prefactors to the long-range decay of the surface charge correlation functions for all possible media (conductor, dielectric, vacuum) configurations. The main result is that the time-dependent quantum prefactor in the retarded regime takes its static classical form, for any temperature.

cond-mat.stat-mech↗

arXiv2008

Equilibrium long-ranged charge correlations at the surface of a conductor coupled to the electromagnetic radiation II

Results of a previous article with the same title are retrieved by a different method. A one-component plasma is bounded by a plane surface. The plasma is fully coupled to the electromagnetic field, therefore the charge correlations are retarded. The quantum correlation function of the surface charge densities, at times different by $t$, at asymptotical large distances $R$, at inverse temperature $β$, decays as $-1/(8π^2βR^3)$, a surprisingly simple result: the decay is independent of Planck's constant $\hbar$ and of the time difference $t$. The present paper is based on the analysis of the collective vibration modes of the system.

cond-mat.stat-mech↗

arXiv2005

Casimir force between two ideal-conductor walls revisited

The high-temperature aspects of the Casimir force between two neutral conducting walls are studied. The mathematical model of "inert" ideal-conductor walls, considered in the original formulations of the Casimir effect, is based on the universal properties of the electromagnetic radiation in the vacuum between the conductors, with zero boundary conditions for the tangential components of the electric field on the walls. This formulation seems to be in agreement with experiments on metallic conductors at room temperature. At high temperatures or large distances, at least, fluctuations of the electric field are present in the bulk and at the surface of a particle system forming the walls, even in the high-density limit: "living" ideal conductors. This makes the enforcement of the inert boundary conditions inadequate. Within a hierarchy of length scales, the high-temperature Casimir force is shown to be entirely determined by the thermal fluctuations in the conducting walls, modelled microscopically by classical Coulomb fluids in the Debye-Hückel regime. The semi-classical regime, in the framework of quantum electrodynamics, is studied in the companion letter by P.R.Buenzli and Ph.A.Martin, cond-mat/0506363, Europhys.Lett.72, 42 (2005).

cond-mat.stat-mech↗