Separable-entangled frontier in a bipartite harmonic system

We consider a statistical mixture of two identical harmonic oscillators which is characterized by four parameters, namely, the concentrations (x and y) of diagonal and nondiagonal bipartite states, and their associated thermal-like noises (T/a and T, respectively). The fully random mixture of two spins 1/2 as well as the Einstein-Podolsky-Rosen (EPR) state are recovered as particular instances. By using the conditional nonextensive entropy as introduced by Abe and Rajagopal, we calculate the separable-entangled frontier. Although this procedure is known to provide a necessary but in general not sufficient condition for separability, it does recover, in the particular case x=T=0 (for all a), the 1/3 exact result known as Peres' criterion. This is an indication of reliability of the calculation of the frontier in the entire parameter space. The x=0 frontier remarkably resembles to the critical line associated with standard diluted ferromagnetism where the entangled region corresponds to the ordered one and the separable region to the paramagnetic one. The entangled region generically shrinks for increasing T or increasing a.Comment: 6 pages, 5 figure

Functions of linear operators: Parameter differentiation

We derive a useful expression for the matrix elements $[\frac{\partial f[A(t)]}{\partial t}]_{i j}$ of the derivative of a function $f[A(t)]$ of a diagonalizable linear operator $A(t)$ with respect to the parameter $t$. The function $f[A(t)]$ is supposed to be an operator acting on the same space as the operator $A(t)$. We use the basis which diagonalizes A(t), i.e., $A_{i j}=\lambda_i \delta_{i j}$, and obtain $[\frac{\partial f[A(t)]}{\partial t}]_{i j}=[\frac{\partial A}{\partial t}]_ {i j}\frac{f(\lambda_j) - f(\lambda_i)} {\lambda_j - \lambda_i}$. In addition to this, we show that further elaboration on the (not necessarily simple) integral expressions given by Wilcox 1967 (who basically considered $f[A(t)]$ of the exponential type) and generalized by Rajagopal 1998 (who extended Wilcox results by considering $f[A(t)]$ of the $q$-exponential type where $\exp_q(x) \equiv [1+(1-q)x]^{1/(1-q)}$ with $q \in {\cal {R}}$; hence, $\exp_1 (x)=\exp(x))$ yields this same expression. Some of the lemmas first established by the above authors are easily recovered.Comment: No figure

Bulk Mediated Surface Diffusion: The Infinite System Case

An analytical soluble model based on a Continuous Time Random Walk (CTRW) scheme for the adsorption-desorption processes at interfaces, called bulk-mediated surface diffusion, is presented. The time evolution of the effective probability distribution width on the surface is calculated and analyzed within an anomalous diffusion framework. The asymptotic behavior for large times shows a sub-diffusive regime for the effective surface diffusion but, depending on the observed range of time, other regimes may be obtained. Montecarlo simulations show excellent agreement with analytical results. As an important byproduct of the indicated approach, we present the evaluation of the time for the first visit to the surface.Comment: 15 pages, 7 figure

Bulk Mediated Surface Diffusion: Finite System Case

We address the dynamics of adsorbed molecules (a fundamental issue in surface physics) within the framework of a Master Equation scheme, and study the diffusion of particles in a finite cubic lattice whose boundaries are at the $z=1$ and the $z=L$ planes where $L = 2,3,4,...$, while the $x$ and $y$ directions are unbounded. As we are interested in the effective diffusion process at the interface $z = 1$, we calculate analytically the conditional probability for finding the system on the $z=1$ plane as well as the surface dispersion as a function of time and compare these results with Monte Carlo simulations finding an excellent agreement.Comment: 19 pages, 8 figure

Electrostatic potential: A new approach for some mixed boundary value problems

A new approach to the solution of problems of electrostatics, some of them with mixed boundary conditions, is presented. The proposed scheme can be used in cases were we have a formal solution in the form of a series in Legendre polynomials and the boundary or matching conditions are given not on the whole interval (0, π) of the polar variable, θ, but only over the interval (0, π/2) or (π/2, π). Truncation of the series after the Nth term and the projection on the subspace generated by the set of the first N even (or odd) Legendre polynomials allows us to determine the unknown coefficients of the approximate solution. The results show rapid convergence toward the exact values as we increase the number of terms, N, included in the approximate solutions. The procedure allows to solve approximately some problems whose exact solutions, we believe, are not yet known.Fil: Prato, Domingo Pedro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; ArgentinaFil: Aguirre Varela, Guillermo Gabriel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentin

Nonextensive Statistical Mechanics: Some Links with Astronomical Phenomena

A variety of astronomical phenomena appear to not satisfy the ergodic hypothesis in the relevant stationary state, if any. As such, there is no reason for expecting the applicability of Boltzmann–Gibbs (BG) statistical mechanics. Some of these phenomena appear to follow, instead, nonextensive statistical mechanics. In the same manner that the BG formalism is based on the entropy SBG = −k∑ipi ln pi, the nonextensive one is based on the form Sq = k(1 −∑ipiq)/(q− 1) (with S₁ = SBG). The stationary states of the former are characterized by an exponential dependence on the energy, whereas those of the latter are characterized by an (asymptotic) power law. A brief review of this theory is given here, as well as of some of its applications, such as the solar neutrino problem, polytropic self-gravitating systems, galactic peculiar velocities, cosmic rays and some cosmological aspects. In addition to these, an analogy with the Keplerian elliptic orbits versus the Ptolemaic epicycles is developed, where we show that optimizing Sq with a few constraints is equivalent to optimizing SBG with an infinite number of constraints.Facultad de Ciencias Astronómicas y Geofísica

A nonextensive critical phenomenon scenario for quantum entanglement

We discuss the paradigmatic bipartite spin-1/2 system having the probabilities $\frac{1+3x}{4}$ of being in the Einstein-Podolsky-Rosen fully entangled state $|\Psi^-$$> \equiv \frac{1}{\sqrt 2}(|$$\uparrow>_A|$$\downarrow>_B$$-|$$\downarrow>_A|$$\uparrow>_B)$ and $\frac{3(1-x)}{4}$ of being orthogonal. This system is known to be separable if and only if $x\le1/3$ (Peres criterion). This critical value has been recently recovered by Abe and Rajagopal through the use of the nonextensive entropic form $S_q \equiv \frac{1- Tr \rho^q}{q-1} (q \in \cal{R};$$S_1$$= -$ $Tr$ $\rho \ln \rho)$ which has enabled a current generalization of Boltzmann-Gibbs statistical mechanics. This result has been enrichened by Lloyd, Baranger and one of the present authors by proposing a critical-phenomenon-like scenario for quantum entanglement. Here we further illustrate and discuss this scenario through the calculation of some relevant quantities.Comment: To appear in Physica A, Proceedings of the IUPAP Workshop on New Trends on Fractal Aspects of Complex Systems (16 - 20 October 2000, Maceio-AL, Brazil), ed. M.L. Lyra (Elsevier, Amsterdam, 2001); 8 PS figure

Foot-and-Mouth Disease Virus Persists in the Light Zone of Germinal Centres

Foot-and-mouth disease virus (FMDV) is one of the most contagious viruses of animals and is recognised as the most important constraint to international trade in animals and animal products. Two fundamental problems remain to be understood before more effective control measures can be put in place. These problems are the FMDV “carrier state” and the short duration of immunity after vaccination which contrasts with prolonged immunity after natural infection. Here we show by laser capture microdissection in combination with quantitative real-time reverse transcription polymerase chain reaction, immunohistochemical analysis and corroborate by in situ hybridization that FMDV locates rapidly to, and is maintained in, the light zone of germinal centres following primary infection of naïve cattle. We propose that maintenance of non-replicating FMDV in these sites represents a source of persisting infectious virus and also contributes to the generation of long-lasting antibody responses against neutralising epitopes of the virus

Uniform function constants of motion and their first-order perturbation

The main purpose of this work is to present some uniform functions constant of the motion, either than the well known quantities arising from spacetime symmetries. These constants are usually associated with intrinsic characteristic of the trajectories of a particle in a central potential field. We treat two cases. The first one is the Lenz vector which sometimes is found in the literature[1, 2]; the other case is associated with the isotropic harmonic oscillator, of relative importance in some simple models of classical molecular interaction. The first example is applied to describe the perturbation of the trajectories in the Rutherford scattering and the precession of the Keplerian orbit of a planet. In the other case the conserved quantity is a symmetric tensor. We find the eigenvectors and eigenvalues of that tensor while at the same time we obtain the solution to the problem of calculating the rotation rate of the orbits in first order of a perturbation parameter in the potential energy, by performing a simple coordinate transformation in the Cartesian plane. We think that the present work addresses to many aspects of Mechanics with a didactical interest in other Physics or Mathematics courses.Fil: Prato, Domingo Pedro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; ArgentinaFil: Hamity, Victor Hugo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin