41,666 research outputs found
Green's function approach to Chern-Simons extended electrodynamics: an effective theory describing topological insulators
Boundary effects produced by a Chern-Simons (CS) extension to electrodynamics
are analyzed exploiting the Green's function (GF) method. We consider the
electromagnetic field coupled to a -term in a way that has been
proposed to provide the correct low energy effective action for topological
insulators (TI). We take the -term to be piecewise constant in
different regions of space separated by a common interface , to be
called the -boundary. Features arising due to the presence of the
boundary, such as magnetoelectric effects, are already known in CS extended
electrodynamics and solutions for some experimental setups have been found with
specific configuration of sources. In this work we illustrate a method to
construct the GF that allows to solve the CS modified field equations for a
given -boundary with otherwise arbitrary configuration of sources. The
method is illustrated by solving the case of a planar -boundary but can
also be applied for cylindrical and spherical geometries for which the
-boundary can be characterized by a surface where a given coordinate
remains constant. The static fields of a point-like charge interacting with a
planar TI, as described by a planar discontinuity in , are calculated
and successfully compared with previously reported results. We also compute the
force between the charge and the -boundary by two different methods,
using the energy momentum tensor approach and the interaction energy calculated
via the GF. The infinitely straight current-carrying wire is also analyzed
Approximation on Nash sets with monomial singularities
This paper is devoted to the approximation of differentiable semialgebraic
functions by Nash functions. Approximation by Nash functions is known for
semialgebraic functions defined on an affine Nash manifold M, and here we
extend it to functions defined on Nash subsets X of M whose singularities are
monomial. To that end we discuss first "finiteness" and "weak normality" for
such sets X. Namely, we prove that (i) X is the union of finitely many open
subsets, each Nash diffeomorphic to a finite union of coordinate linear
varieties of an affine space and (ii) every function on X which is Nash on
every irreducible component of X extends to a Nash function on M. Then we can
obtain approximation for semialgebraic functions and even for certain
semialgebraic maps on Nash sets with monomial singularities. As a nice
consequence we show that m-dimensional affine Nash manifolds with divisorial
corners which are class k semialgebraically diffeomorphic, for k>m^2, are also
Nash diffeomorphic.Comment: 39 page
Electro and magneto statics of topological insulators as modeled by planar, spherical and cylindrical boundaries: Green function approach
The Green function (GF) method is used to analyze the boundary effects
produced by a Chern Simons (CS) extension to electrodynamics. We consider the
electromagnetic field coupled to a term that is piecewise constant in
different regions of space, separated by a common interface , the
boundary, model which we will refer to as electrodynamics
( ED). This model provides a correct low energy effective action for
describing topological insulators (TI). In this work we construct the static GF
in ED for different geometrical configurations of the
boundary, namely: planar, spherical and cylindrical interfaces. Also
we adapt the standard Green theorem to include the effects of the
boundary. These are the most important results of our work, since they allow to
obtain the corresponding static electric and magnetic fields for arbitrary
sources and arbitrary boundary conditions in the given geometries. Also, the
method provides a well defined starting point for either analytical or
numerical approximations in the cases where the exact analytical calculations
are not possible. Explicit solutions for simple cases in each of the
aforementioned geometries for boundaries are provided. The adapted
Green theorem is illustrated by studying the problem of a point like electric
charge interacting with a planar TI with prescribed boundary conditions. Our
generalization, when particularized to specific cases, is successfully compared
with previously reported results, most of which have been obtained by using the
methods of images.Comment: 24 pages, 4 figures, accepted for publication in PRD. arXiv admin
note: text overlap with arXiv:1511.0117
Noncommutative spacetime symmetries: Twist versus covariance
We prove that the Moyal product is covariant under linear affine spacetime
transformations. From the covariance law, by introducing an -space
where the spacetime coordinates and the noncommutativity matrix components are
on the same footing, we obtain a noncommutative representation of the affine
algebra, its generators being differential operators in -space. As
a particular case, the Weyl Lie algebra is studied and known results for Weyl
invariant noncommutative field theories are rederived in a nutshell. We also
show that this covariance cannot be extended to spacetime transformations
generated by differential operators whose coefficients are polynomials of order
larger than one. We compare our approach with the twist-deformed enveloping
algebra description of spacetime transformations.Comment: 19 pages in revtex, references adde
Energy partition and segregation for an intruder in a vibrated granular system under gravity
The difference of temperatures between an impurity and the surrounding gas in
an open vibrated granular system is studied. It is shown that, in spite of the
high inhomogeneity of the state, the temperature ratio remains constant in the
bulk of the system. The lack of energy equipartition is associated to the
change of sign of the pressure diffusion coefficient for the impurity at
certain values of the parameters of the system, leading to a segregation
criterium. The theoretical predictions are consistent with previous
experimental results, and also in agreement with molecular dynamics simulation
results reported in this paper.Comment: To appear in Phys. Rev. Let
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