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Title:
Quantum Entanglement with Gaussian states
Author:
J. P. Singh
Comments:
16 pages, no figures
Abstract:
Quantum Entanglement is an intriguing phenomenon that has been mystifying physicists ever since Einstein, Podoloky & Rosen published their gedanken experiment in 1935. It is now widely believed that quantum entanglement could be the cardinal resource in quantum communication, quantum computing and other information processing activities. Such phenomena are set to revolutionize the world of information technology. In this article, after briefly elucidating the Peres Separability Criterion for discrete and continuous variable systems, we explicitly compute the various elements of the Covariance Matrix (CM) for Gaussian states on the one dimensional and two dimensional manifolds and obtain expression for the normal and symplectic eigenvalues for applying the above criterion of separability. We, finally, extend this formalism to the case of non-commuting spatial coordinates making use of the fact that the ground state eigenfunctions of the harmonic oscillator happen to be Gaussian functions.
Title:
n-Lie algebras
Author:
M. Goze, N. Goze, E. Remm
Comments:
12 pages, no figures
Abstract:
The notion of n-ary algebras, that is vector spaces with a multiplication concerning n-arguments, n \geq 3, became fundamental since the works of Nambu. Here we first present general notions concerning n-ary algebras and associative n-ary algebras. Then we will be interested in the notion of n-Lie algebras, initiated by Filippov, and which is attached to the Nambu algebras. We study the particular case of nilpotent or filiform n-Lie algebras to obtain a beginning of classification. This notion of n-Lie algebra admits a natural generalization in Strong Homotopy n-Lie algebras in which the Maurer Cartan calculus is well adapted.
Title:
Exact Solution Of MHD Free Convection Flow And Mass Transfer Near A Moving Vertical Plate In Presence Of Thermal Radiation
Author:
K. Das
Comments:
13 pages, 12 figures
Abstract:
The objective of this paper is to study the MHD unsteady free convection flow and mass transfer of a viscous, electrically conducting incompressible fluid in presence of thermal radiation and under the influence of uniform magnetic field applied normal to the plate near an infinite vertical plate, which moves with time dependent velocity. The fluid is also assumed to be gray; emitting absorbing but non scattering medium and the optically thick radiation limit is considered. The solutions of the present problem are obtained in closed form by Laplace transform technique and the expressions for velocity, temperature, concentration , skin friction, rate of heat and mass transfer has been obtained. Some important applications of physical interest for different type motion of the plate are discussed. The results obtained have also been presented numerically through graphs to observe the effects of various parameters and the physical aspects of the problem.
Title:
On The Memory Of Non-Locally Damped Harmonic Oscillator
Author:
A. N. Ikot, E. J. Uwah, L. E. Akpabio, I. O. Akpan.
Comments:
8 pages, no figures
Abstract:
We investigate the equation of motion for damped oscillator with arbitrary time memory. We show that the classical dynamics which breaks down the local composition law still preserved the basic uncertainty relation. The propagator and the wavefunction of the system is also evaluated.
Title:
Some properties of Newton polygons of polynomial ordinary differential equations
Author:
A. Ayad
Comments:
5 pages, no figures
Abstract:
We show in this paper some properties of the Newton polygon of a polynomial ordinary differential equation. We give the relation between the Newton polygons of a differential polynomial and its partial derivatives. Newton polygons of sums and evaluations of differential polynomials are also described.
Title:
The Central Disintegration Measure Of The Regular Representation On Non Unimodular Locally Compact Group
Author:
K.Sammad, M.Akkouchi, A.Bakali, S.Kabbaj
Comments:
9 pages, no figures
Abstract:
The article generalizes to non-unimodular locally compact groups some basic facts that were previously only known in the unimodular case. The main results concern Gelfand measures, they determine the support of the central disintegration measure of the natural regular representation. The proof of this result uses the notion of \mu-non-degeneracy of representations.
Title:
MHD Mixed Convection Boundary Layer Flow with Double Diffusion and Thermal Radiation adjacent to a Vertical Permeable Surface Embedded in a Porous Medium
Author:
S. S. Tak, A. Khan, R. Mathur
Comments:
11 pages, 4 figures
Abstract:
The effects of lateral mass flux, thermal radiation, transverse magnetic field and double diffusion (Soret and Dufour effects) on heat and mass transfer in a mixed convection boundary layer flow over a heated vertical surface embedded in Darcian porous media have been studied. The Rosseland approximation for the radiative heat flux is used in the energy equation. It is found that the similarity solution exists in the present case. The resulting set of coupled non-linear ordinary differential equations is solved numerically using shooting technique. Dimensionless velocity, temperature and concentration profiles are presented graphically against \eta for various values of the mixed convection parameter RP. The numerical values of local Nusselt number and local Sherwood number have been tabulated for various values of involved parameters and discussed in detail.
Title:
Algebraic points on some Fermat curves and some quotients of Fermat curves: Progress
Author:
O. Sall
Comments:
5 pages, no figures
Abstract:
In this work we speak about progress of research on the algebraic points on some curves. The main results completes previous works obtained on some Fermat curves and their quotients.
Title:
The conformal invariance of the Poisson-Lie group SU(2) by dressing transformation
Author:
M.W.Mansouri, B. Ganbouri
Comments:
6 pages, no figures
Abstract:
We show the conformal invariance of the Poisson-Lie group SU(2) by dressing transformations. This construction gives in particular a Poisson cohomology class of the group SU(2).
Title:
Brownian dynamics of nanoparticles in contact with a confined
biomembrane
Author:
Y. Madmoune, K. El Hasnaoui, A. Bendouch, H. Kaidi, M. Chahid, and
M. Benhamou
Comments:
10 pages, 2 figures
Abstract:
The system we consider is a fluid membrane confined to two parallel
reflecting walls that are separated by a finite distance, L,
assumed to be small in comparison to the bulk roughness. The
attractive membrane is surrounded by small colloidal particles
(nanoparticles). The purpose is the study of Brownian dynamics of
these particles, under a change of a suitable parameter, such as
temperature, T, or colloid-membrane interaction strength, w. The
Brownian dynamics is investigated through the knowledge of the time
particle density, which solves the Smoluchowski equation. Solving
this equation around the mid-plane, where the essential of
phenomenon occurs, we obtain the {\em exact form} of the local
particle density, as a function of the perpendicular distance and
time. In the derived expression, appears some time-scale, \tau,
which scales as \tau \thicksim L^3/w. This scale-time can be
interpreted as the required time over which the colloidal suspension
reaches their final equilibrium state. Also, \tau can be regarded
as the time-interval over which the particles are trapped in holes
and valleys.
Title:
Casimir force in confined biomembranes
Author:
K. El Hasnaoui, Y. Madmoune, H. Kaidi, M. Chahid, and M. Benhamou
Comments:
14 pages, 3 figures
Abstract:
We reexamine the computation of the Casimir force between two
parallel interacting plates delimitating a liquid with an immersed
biomembrane. We denote by D their separation, which is assumed to
be much smaller than the bulk roughness, in order to ensure the
membrane confinement. This repulsive force originates from the
thermal undulations of the membrane. To this end, we first introduce
a field theory, where the field is noting else but the
height-function. The field model depends on two parameters, namely
the membrane bending rigidity constant, \kappa, and some elastic
constant, \mu \thicksim D^{-4}. We first compute the static
Casimir force (per unit area), \Pi, and find that the latter
decays with separation D as: \Pi \thicksim D^{-3}, with a known
amplitude scaling as \kappa ^{-1}. Therefore, the force has
significant values only for those biomembranes of small enough
\kappa. Second, we consider a biomembrane (at temperature T)
that is initially in a flat state away from thermal equilibrium, and
we are interested in how the dynamic force, \Pi (t),
grows in time.
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