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Electronic oscillations in paired polyacetylene chains
An interacting pair of polyacetylene chains are initially modeled as a couple
of undimerized polymers described by a Hamiltonian based on the tight-binding
model representing the electronic behavior along the linear chain, plus a
Dirac's potential double well representing the interaction between the chains.
A theoretical field formalism is employed, and we find that the system exhibits
a gap in its energy band due to the presence of a mass-matrix term in the
Dirac's Lagrangian that describes the system. The Peierls instability is
introduced in the chains by coupling a scalar field to the fermions of the
theory via spontaneous symmetry breaking, to obtain a kink-like soliton, which
separates two vacuum regions, i.e., two spacial configurations (enantiomers) of
the each molecule. Since that mass-matrix and the pseudo-spin operator do not
commute in the same quantum representation, we demonstrate that there is a
particle oscillation phenomenon with a periodicity equivalent to the Bloch
oscillations.Comment: 4 pages, 1 figure.to appear in Solid State Communication
Casimir Effect in the Rainbow Einstein's Universe
In the present paper we investigate the effects caused by the modification of
the dispersion relation obtained by solving the Klein-Gordon equation in the
closed Einstein's universe in the context of rainbow's gravity models. Thus, we
analyse how the quantum vacuum fluctuations of the scalar field are modified
when compared with the results obtained in the usual General Relativity
scenario. The regularization, and consequently the renormalization, of the
vacuum energy is performed adopting the Epstein-Hurwitz and Riemann's zeta
functions.Comment: 15 pages, 1 figure. To appear in Europhysics Letter
On Effective Spacetime Dimension in the Ho\v{r}ava-Lifshitz Gravity
In this manuscript we explicitly compute the effective dimension of spacetime
in some backgrounds of Ho\v{r}ava-Lifshitz (H-L) gravity. For all the cases
considered, the results are compatible with a dimensional reduction of the
spacetime to , at high energies (ultraviolet limit), which is confirmed
by other quantum gravity approaches, as well as to , at low energies
(infrared limit). This is obtained by computing the free energy of massless
scalar and gauge fields. We find that the only effect of the background is to
change the proportionality constant between the internal energy and
temperature. Firstly, we consider both the non-perturbative and perturbative
models involving the matter action, without gravitational sources but with
manifest time and space symmetry breaking, in order to calculate modifications
in the Stephan-Boltzmann law. When gravity is taken into account, we assume a
scenario in which there is a spherical source with mass and radius in
thermal equilibrium with radiation, and consider the static and spherically
symmetric solution of the H-L theory found by Kehagias-Sfetsos (K-S), in the
weak and strong field approximations. As byproducts, for the weak field regime,
we used the current uncertainty of the solar radiance measurements to establish
a constraint on the free parameter of the K-S solution. We also
calculate the corrections, due to gravity, to the recently predicted attractive
force that black bodies exert on nearby neutral atoms and molecules.Comment: references adde
Photon mass as a probe to extra dimensions
In this manuscript we show that the geometrical localization mechanism
implies a four dimensional mass for the photon. The consistence of the model
provides a mass given exactly by where is the Ricci
scalar. As a consequence, the cosmological photon has a mass related to the
vacuum solution of the Einstein equation. At the present age of the universe we
have a dS vacuum with , where Lambda is a positive cosmological
constant. With this we find that kg, which
is below the present experimental upper bounds, and such correction may be
observed in the next years with more precise measurements. By considering the
value of inside some astrophysical sources and environments we find that
the bound is also satisfied. The experimental verification of this mass, beyond
pointing to the existence of extra dimensions, would imply in a fundamental
change in cosmology, astrophysics and in particle physics since the same
mechanism is valid for non-abelian gauge fields.Comment: 4 page
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