arXiv subjects

G. Tellez

Publications and source records attributed to G. Tellez.

10 recordsLinked to original sources

arXiv2013

Exact and asymptotic features of the edge density profile for the one component plasma in two dimensions

There is a well known analogy between the Laughlin trial wave function for the fractional quantum Hall effect, and the Boltzmann factor for the two-dimensional one-component plasma. The latter requires analytic continuation beyond the finite geometry used in its derivation. We consider both disk and cylinder geometry, and focus attention on the exact and asymptotic features of the edge density. At the special coupling Γ:= q^2/k_BT=2 the system is exactly solvable. In particular the k-point correlation can be written as a k \times k determinant, allowing the edge density to be computed to first order in Γ- 2. A double layer structure is found, which in turn implies an overshoot of the density as the edge of the leading support is approached from inside the plasma. Asymptotic analysis shows that the deviation from the leading order (step function) value is different for into the plasma than for outside. For general Γ, a Gaussian fluctuation formula is used to study the large deviation form of the density for N large but finite. This asymptotic form involves thermodynamic quantities which we independently study, and moreover an appropriate scaling gives the asymptotic decay of the limiting edge density outside of the plasma.

cond-mat.stat-mech↗

arXiv2009

Crossover Between Organized and Disorganized States In Some Non-Equilibrium Systems

We study numerically the crossover between organized and disorganized states of three non-equilibrium systems: the Poisson/coalesce random walk (PCRW), a one-dimensional spin system and a quasi one-dimensional lattice gas. In all cases, we describe this crossover in terms of the average spacing between particles/domain borders $< S(t) >$ and the spacing distribution functions $p^{(n)}(s)$. The nature of the crossover is not the same for all systems, however, we found that for all systems the nearest neighbor distribution $p^{(0)}(s)$ is well fitted by the Berry-Robnik model. The destruction of the level repulsion in the crossover between organized an disorganized states is present in all systems. Additionally, we found that the correlations between domains in the gas and spin systems are not strong and can be neglected in a first approximation but for the PCRW the correlations between particles must be taken into account. To find $p^{(n)}(s)$ with $n>1$, we propose two different analytical models based on the Berry-Robnik model. Our models give us a good approximation for the statistical behavior of these systems in their crossover and allow us to quantify the degree of order/disorder of the system.

cond-mat.stat-mech↗

arXiv2007

Preferential interaction coefficient for nucleic acids and other cylindrical poly-ions

The thermodynamics of nucleic acid processes is heavily affected by the electric double-layer of micro-ions around the polyions. We focus here on the Coulombic contribution to the salt-polyelectrolyte preferential interaction (Donnan) coefficient and we report extremely accurate analytical expressions valid in the range of low salt concentration (when polyion radius is smaller than the Debye length). The analysis is performed at Poisson-Boltzmann level, in cylindrical geometry, with emphasis on highly charged poly-ions (beyond ``counter-ion condensation''). The results hold for any electrolyte of the form $z_-$:$z_+$. We also obtain a remarkably accurate expression for the electric potential in the vicinity of the poly-ion.

cond-mat.soft↗

arXiv2006

Exact asymptotic expansions for the cylindrical Poisson-Boltzmann equation

The mathematical theory of integrable Painleve/Toda type systems sheds new light on the behavior of solutions to the Poisson-Boltzmann equation for the potential due to a long rod-like macroion. We investigate here the case of symmetric electrolytes together with that of 1:2 and 2:1 salts. Short and large scale features are analyzed, with a particular emphasis on the low salinity regime. Analytical expansions are derived for several quantities relevant for polyelectrolytes theory, such as the Manning radius. In addition, accurate and practical expressions are worked out for the electrostatic potential, which improve upon previous work and cover the full range of radial distances.

cond-mat.soft↗

arXiv1999

Exact Finite Size Study of the 2dOCP at Gamma=4 and Gamma=6

An exact numerical study is undertaken into the finite $N$ calculation of the free energy and distribution functions for the two-dimensional one-component plasma. Both disk and sphere geometries are considered, with the coupling $Γ$ set equal to 4 and 6. Extrapolation of our data for the free energy is consistent with the existence of a universal term ${χ\over 12} \log N$, where $χ$ denotes the Euler characteristic of the surface, as predicted theoretically. The exact finite $N$ density profile is shown to give poor agreement with the contact theorem relating the density at contact and potential drop to the pressure in the thermodynamic limit. This is understood theoretically via a known finite $N$ version of the contact theorem. Furthermore, the ideas behind the derivation of the latter result are extended to give a sum rule for the second moment of the pair correlation in the finite disk, which in the thermodynamic limit converges to the Stillinger-Lovett result.

cond-mat.stat-mech↗

arXiv1998

Two-dimensional Coulomb systems on a surface of constant negative curvature

We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to zero at infinity. The pressure can be expanded as a series in integer powers of the density (the virial expansion). The correlation functions have a thermodynamic limit, and remarkably that limit is the same one for the Coulomb interaction and some other interaction law. However, special care is needed for defining a thermodynamic limit of the free energy density. There are sum rules expressing the property of perfect screening. These generic properties can be checked on the Debye-Hückel approximation, and on two exactly solvable models~: the one-component plasma and the two-component plasma, at some special temperature.

cond-mat↗

arXiv1996

Collective modes and correlations in one-component plasmas

The static and time-dependent potential and surface charge correlations in a plasma with a boundary are computed for different shapes of the boundary. The case of a spheroidal or spherical one-component plasma is studied in detail because experimental results are available for such systems. Also, since there is some knowlegde both experimental and theoretical about the electrostatic collective modes of these plasmas, the time-dependent correlations are computed using a method involving these modes.

cond-mat↗

arXiv1995

The Ideal Conductor Limit

This paper compares two methods of statistical mechanics used to study a classical Coulomb system S near an ideal conductor C. The first method consists in neglecting the thermal fluctuations in the conductor C and constrains the electric potential to be constant on it. In the second method the conductor C is considered as a conducting Coulomb system the charge correlation length of which goes to zero. It has been noticed in the past, in particular cases, that the two methods yield the same results for the particle densities and correlations in S. It is shown that this is true in general for the quantities which depend only on the degrees of freedom of S, but that some other quantities, especially the electric potential correlations and the stress tensor, are different in the two approaches. In spite of this the two methods give the same electric forces exerted on S.

cond-mat↗

arXiv1995

Universality in some classical Coulomb systems of restricted dimension

Coulomb systems in which the particles interact through the $d$-dimensional Coulomb potential but are confined in a flat manifold of dimension $d - 1$ are considered. The Coulomb potential is defined with some boundary condition involving a characteristic macroscopic distance $W$ in the direction perpendicular to the manifold~: either it is periodic of period $W$ in that direction, or it vanishes on one ideal conductor wall parallel to the manifold at a distance $W$ from it, or it vanishes on two parallel walls at a distance $W$ from each other with the manifold equidistant from them. Under the assumptions that classical equilibrium statistical mechanics is applicable and that the system has the macroscopic properties of a conductor, it is shown that the suitably smoothed charge correlation function is universal, and that the free energy and the grand potential have universal dependences on $W$ (universal means independent of the microscopic detail). The cases $d = 2$ are discussed in detail, and the generic results are checked on an exactly solvable model. The case $d = 3$ of a plane parallel to an ideal conductor is also explicitly worked out.

cond-mat↗

arXiv1995

Coulomb Systems Seen as Critical Systems: Ideal Conductor Boundaries

The grand potential of a classical Coulomb system has universal finite-size corrections similar to the ones which occur in the free energy of a simple critical system : the massless Gaussian field. Here, the Coulomb system is assumed to be confined by walls made of an ideal conductor material; this choice corresponds to simple (Dirichlet) boundary conditions for the Gaussian field. For a $d$-dimensional ($d>or=2$) Coulomb system confined in a slab of thickness $W$, the grand potential (in units of $kT$) per unit area has the universal term $Gamma(d/2) zeta(d)/2^d pi^{d/2}W^{d-1}$. For a two-dimensional Coulomb system confined in a disk of radius $R$, the grand potential (in units of $kT$) has the universal term $(1/6) ln R$. These results, of general validity, are checked on two-dimensional solvable models.

cond-mat↗