Entanglement concentration using quantum statistics

We propose an entanglement concentration scheme which uses only the effects of quantum statistics of indistinguishable particles. This establishes the fact that useful quantum information processing can be accomplished by quantum statistics alone. Because of the basis independence of statistical effects, our protocol requires less knowledge of the initial state than most entanglement concentration schemes. Moreover, no explicit controlled operation is required at any stage.     

Wetting at the grain boundary in the planar Ising model

In this paper the conditions of pinning of an interface in a 2D Ising ferromagnet with defect connections in a solid-on-solid (SOS) limit are given. It is known that in this case the localisation of interface is formally equivalent to the bound state of quantum particle in temperature dependent effective potential. We show that a wetting transition occurs whenever the couplings on the two sides of the defect are different.     

Correlation between C-H and C-C spin-spin coupling constants and s character of hybrids calculated by the maximum overlap method

For some thirty hydrocarbons the s character of hybrids obtained by the application of the maximum overlap method have been correlated with C-H and C-C spin-spin coupling constants. The following relationships were obtained: $$J_{{\text{C}}^{{\text{13}}} - {\text{H}}} = 1079a_{{\text{CH}}}^{\text{2}} /(1 + S_{{\text{CH}}}^{\text{2}} ) - 54.9$$ , $$J_{{\text{C}}_{\text{1}}^{{\text{13}}} - {\text{C}}_{\text{2}}^{{\text{13}}} } = 1020.5a_{{\text{C}}_{\text{1}} }^2 a_{{\text{C}}_{\text{2}} }^{\text{2}} /(1 + S_{{\text{CC}}}^{\text{2}} ) - 8.2$$ . Here the coupling constants are expressed in cps units. In the calculation of the maximum overlap hybrids either the experimental bond lengths or a standard bond lengths were used. For the \(J_{{\text{C}}^{{\text{13}}} - {\text{H}}}\) and \(J_{{\text{C}}^{{\text{13}}} - {\text{H}}} \) coupling constants the standard deviations are 0.9 cps and 1.9 cps respectively. It has been suggested that the large additive constant in the \(J_{{\text{C}}^{{\text{13}}} - {\text{H}}}\) correlation may be attributed to the ionic character of C-H bonds. A good agreement with the experimental data strongly supports the idea that the Fermi contact term and the hybridization are dominant factors in determining carbon-hydrogen and carbon-carbon spin-spin coupling constants across one bond, at least in hydrocarbons.     

Exact treatment of generalized modifications of finite-dimensional systems by the LRM approach

LRM (Low Rank Modification) is a mathematical method that produces eigenvalues and eigenstates of generalized eigenvalue equations. It is similar to the perturbation expansion in that it assumes the knowledge of the eigenvalues and eigenstates of some related (unperturbed) system. However, unlike perturbation expansion, LRM produces correct results however large the modification of the original system. LRM of finite-dimensional systems is here generalized to the combined (external and internal) modifications. Parent n-dimensional system A _n containing n eigenvalues λ _i and n eigenstates \({| {\Phi_i}\rangle}\) is described by the generalized n × n eigenvalue equation. In an external modification system A _n interacts with another ρ-dimensional system B _ρ which is situated outside the system A _n . In an internal modification relatively small σ-dimensional subsystem of the parent system A _n is modified. Modified system C _n+ρ that contains external as well as internal modifications is described by the generalized (n + ρ) × (n + ρ) eigenvalue equation. This system has (n + ρ) eigenvalues \({\varepsilon_s}\) and (n + ρ) corresponding eigenstates \({| {\Psi_s}\rangle}\) . In LRM this generalized (ρ + n) × (ρ + n) eigenvalue equation is replaced with a (nonlinear) (ρ + σ) × (ρ + σ) equation which produces all eigenvalues \({\varepsilon_s \notin \left\{ {\lambda_i}\right\}}\) and all the corresponding eigenstates \({| {\Psi_s}\rangle }\) of C _{n + ρ}. Another equation produces remaining solutions (if any) that satisfy \({\varepsilon_s \in \left\{ {\lambda_i}\right\}}\) . Those two equations produce exact solution of the modified system C _{n + ρ}. If (ρ + σ) is small with respect to n, this approach is numerically much more efficient than a standard diagonalization of the original generalized eigenvalue equation. Unlike perturbation expansion, LRM produces exact results, however large modification of the parent system A _n .     

Rational summation ofp-adic series

The problem of rational summation for a wide class ofp-adic convergent series is considered. Here, rational summation refers to the method of obtaining the rational sum of a power series for a rational value of its variable. A formula suitable for this summation is derived. Conditions for rational summability are obtained. Rational summation is possible only for special forms of the series. It is shown that the inverse problem of rational summation is always solvable. This is illustrated by some characteristic examples. Possible rational (adelic) summation of divergent perturbative expansions in string theory, and quantum field theory, is discussed.Institute of Physics, P.O. Box 57, 11001 Belgrade, Yugoslavia. Published in Toereticheskaya i Matematicheskaya Fizika, Vol. 100, No. 3, pp. 342–353, September, 1994.     

A one-dimensional numerical model of heat and mass transfer in air-water droplet flow

This paper presents a one-dimensional numerical model of the heat, mass and momentum transfer between water droplets and humid air in the disperse process device. The model merges a model of the disintegration of a water sheet presented by Dombrowski et al. [1] and a one-dimensional numerical model of the transport phenomena in the air washer presented by Demird?i? et al. [10]. Numerical results are compared with the available experimental results. Numerical simulations can predict one-dimensional analysis of the geometrical and thermophysical parameters in the disperse process device.     

Nonlinear wave propagation in binary mixtures of Euler fluids

In the present paper, we study the propagation of acceleration and shock waves in a binary mixture of ideal Euler fluids, assuming that the difference between the atomic masses of the constituents is negligible. We evaluate the characteristic speeds, proving that they can be separated into two groups: one is related to the case of a single Euler fluid, provided that an average ratio of specific heats is introduced; the other is new and related to the propagation speed due to diffusion. We evaluate the critical time for sound acceleration waves and compare its value to that of a single fluid. We then study shock waves, showing that three types of shock waves appear: sonic and contact shocks, which have counterparts in the single fluid case, and the diffusive shock, which is peculiar to the mixture. We discuss the admissibility of the shock waves using the Lax-Liu conditions and the entropy growth criterion. It is proved that the sonic and the characteristic shock obey the same properties as in the single fluid case, while for the diffusive shock there exists a locally exceptional case that is determined by a particular value of the concentration of the constituents, for which the genuine nonlinearity is lost and no shocks are admissible. For other values of the unperturbed concentration, the diffusive shock is stable in a bounded interval of admissibility.Received: 15 December 2002, Accepted: 28 June 2003 Correspondence to: T. RuggeriS. Simi: On leave from the Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, Serbia     

Approximation of thermoelasticity contact problem with nonmonotone friction

The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a nonmonotone and multivalued law. The coupling effect of the problem is neglected. Therefore, the thermic part of the problem is considered independently on the elasticity problem. For the displacement vector, we formulate one substationary problem for a non-convex, locally Lipschitz continuous functional representing the total potential energy of the body. All problems formulated in the paper are approximated with the finite element method.