Title:
A convenient explicit
reduction of Einstein equations in harmonic gauge: Connection with
wave maps type equations
Author:
Calvin Tadmon
Comments:
20 pages, no figures
Abstract:
Using the harmonic coordinates gauge, we derive a convenient and
precise form of the Einstein equations as a quasilinear hyperbolic
system of second order differential equations. The point here is
that this form is much more simpler than those presented by several
authors in previous works. Therefore simplification of some aspects
in the proofs of many known results related to Einstein equations is
foreseeable. Pointwise estimates of the simplified inhomogeneous
terms are established. A natural link between Einstein equations and
wave maps type equations is furnished.
Title:
Squeezing in Floquet States and Quasi-energies of Harmonic Oscillator
Driven by a Strong Periodic Field
Author:
M. Janati-Idrissi, A. Fedoul, Y. Achkar, A. Chatwiti and S. Sayouri
Comments:
10 pages, 5 figures
Abstract:
Floquet theory combined with the resonating averages method (RAM)
gives a direct alternative approach for solving the time-dependent
Schr\"{o}dinger equation of a periodically driven quantum harmonic
oscillator, and lead to analytical solutions, similar to those
published in the literature based on different other methods. The
explicit expressions of the wave functions and the corresponding
quasi-energies, as well as, the variances of position and momentum
are computed. Numerical simulations of the analytic results, is
performed at different parameters values, in an attempt to
elucidate, the dynamic localization and the squeezing properties of
the wave-packet of this system.
Title:
The ladder operators of Rosen-Morse Potential with Centrifugal term by Factorization Method
Author:
A. R. Amani, M. A. Moghrimoazzen, H. Ghorbanpour and S. Barzegaran
Comments:
7 pages, 2 figures
Abstract:
In this paper, we have considered analytical solution of radial
Schrödinger equation with Rosen-Morse potential by factorization
method. In order to obtain bound states, we have approximated the
centrifugal term ($l\neq0$) as exponential function. By using
associated Jacobi polynomial and comparing with radial part, we have
obtained eigenvalues and eigenfunction for l-wave cases. The
factorization method leads us to calculate the first order equations
as the raising and lowering operators. These operators help us to
Hamiltonian system which is written in terms of two first order
differential equation with respect to parameters n and l as the
raising and lowering operators. Finally we have been considered that
there is not shape invariance condition proportional to parameters
n and l. Also the variations of energy spectrum has plotted in
terms of n.
Title:
Brans-Dicke scalar field and de Sitter Relativity
Author:
E. Benedetto
Comments:
9 pages, no figures
Abstract:
In this paper we investigate the problem to satisfy the Mach's
principle in cosmology. Particularly we consider de
Sitter-Fantappiè Relativity and Brans-Dicke theory. These two
approaches, in fact, in natural way seem to incorporate this
principle and the accelerating Universe.
Title:
Gibbs's Measures of a Multi-Colored
Disordered Lattice Gas
Author:
Halim Zeghdoudi and Hacène Boutabia
Comments:
6 pages, no figures
Abstract:
As observed [2] their approach can be generalized to
multi-coloured case for several external chemical potentials . To
this end, we consider a system of colored particles in
$\mathbb{Z}^{d}$ driven by a
disordered Markov generator similar to that of Faggionato and Martinelli [1]. Gibbs's measures are constructed to making dynamics
reversible in time.
Title:
Statistics of a single D-manifold restricted to two parallel
biomembranes or a tubular vesicle
Author:
M. Benhamou, K.
Elhasnaoui, H. Kaidi and M. Chahid
Comments:
10 pages, no figures
Abstract:
The purpose is an extensive conformational study of a single polymer
immersed in an aqueous medium (good solvent) delimitated by bilayer
membranes. To be more general, we assume that the polymer is of
arbitrary topology we term D-polymeric fractal or D-manifold,
where D
is the spectral dimension (for instance, D=1, for linear polymers, and
4/3, for branched ones). The main quantity to consider is the
parallel extension of the confined polymer. To make explicit
calculations, we suppose that the polymer is restricted to a tubular
vesicle or two parallel biomembranes. We first show that, for the
first geometry, the polymer is confined only when the tubular
vesicle is in equilibrium state. For the second geometry, the
confinement is possible if only if the two parallel membranes are in
their binding state, that is below the unbinding or adhesion
temperature. In any case, the parallel gyration radius of the
confined polymer is computed using an extended Flory-de Gennes
theory. As result, this radius strongly depends on the polymer
topology (through the spectral dimension D and on the
membranes sizes, which are the equilibrium diameter (function of
bending modulus, pressure difference between inner and outer sides
of the membrane, and interfacial tension coefficient), for the first
geometry, and the mean-separation (function of temperature and
interaction strength between the adjacent membranes), for the second
one. Finally, we give the expression of the confinement free energy,
as a function of the polymer size, and discuss the effects of
external pressure or lateral tension on the radius expression for
two confining parallel membranes.
Title:
Fractional Oscillator Algebra and q-Deformed Oscillator Algebra
Author:
E.H. El Kinani, M.R. Sidi Ammi and M. Rahmoune
Comments:
6 pages, no figures
Abstract:
In this paper based on the Riemann-Liouville fractional derivatives
we introduce
the fractional oscillator algebra generalized by the fractional mutual operators $a^{\dagger}_{\alpha}$, $a_{\alpha}$
and the fractional operator´s number $N_{\alpha}$ defined in terms of the fractional observables $\hat{X}^{\alpha}$ and $\hat{P}^{\alpha}$.
The connection between the fractional oscillator algebra and the $q$-deformation oscillator algebra is also investgaded.
Title:
Stability and Synchronization Criteria for Parametrically driven oscillators
Author:
Olasunkanmi I. Olusola, Uchechukwu E. Vincent and Abdulahi N. Njah
Comments:
9 pages, 4 figures
Abstract:
In this paper, the stabilty of synchronized dynamics of two linearly
coupled parametrically excited oscillators is studied. Some
necessary and sufficient algebraic criteria for global asymptotic
stability of the synchronous states were derived by means of the
Lyapunov stability theory and linear matrix inequality; and an
estimated threshold coupling, for which synchronization could be
reached was determined. The feasibility of the obtained criteria
with demonstrated via numerical simulation.
Title:
2-dimensional algebras
Author:
Michel Goze
and Elisabeth Remm
Comments:
11 pages, no figures
Abstract:
We classify, up an isomorphism, the 2-dimensional algebras over a
field K. This permits to have easely the classification of
complex 2-dimensional Jordan algebra.
Title:
Kekulé Cycles as 1D Analogue of Graphene: Electronic Properties
Author:
L. B Drissi, E.H Saidi and M. Bousmina
Comments:
23 pages, 10 figures
Abstract:
Using tight binding model and symmetries, we study the electronic
properties of Kekulé cycles thought of as the \emph{1D} analogue
of the graphene monolayer. Focussing on the family C$_{2N}$H$_{2N}$
and thinking about these molecules as the superposition of two
sublattices type C$_{N}$H$_{N}$, we develop the hamiltonian model of
the delocalized electrons and derive a basic constraint relation on
the electronic displacements. It is shown as well that, near the
Dirac points, the delocalized electrons may be approached by a Dirac
theory in (1+1) dimensions.
Title:
Absorption spectrum for a multi-photon $\Xi$-type
three-level atom driven by a binomial field with nonlinearities
Author:
A. A. Eied
Comments:
10 pages, 5 figures
Abstract:
A treatment of a multi-photon $\Xi$-type three-level atom
interacting with a single mode field in a cavity, taking explicitly
the existence of forms of nonlinearities of both the field and the
intensity-dependent atom-field coupling into account. Analytical
expressions of the absorption spectrum is presented using the
dressed states of the system. The characteristics of the absorption
spectrum considering the field to be initially in a binomial state
is exhibited. The effects of the photon multiplicities, mean number
of photons, detuning and the nonlinearities on the spectrum are
investigated.
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