26 research outputs found
Quasinormal modes of plane-symmetric anti-de Sitter black holes: a complete analysis of the gravitational perturbations
We study in detail the quasinormal modes of linear gravitational
perturbations of plane-symmetric anti-de Sitter black holes. The wave equations
are obtained by means of the Newman-Penrose formalism and the Chandrasekhar
transformation theory. We show that oscillatory modes decay exponentially with
time such that these black holes are stable against gravitational
perturbations. Our numerical results show that in the large (small) black hole
regime the frequencies of the ordinary quasinormal modes are proportional to
the horizon radius (wave number ). The frequency of the purely
damped mode is very close to the algebraically special frequency in the small
horizon limit, and goes as in the opposite limit. This result
is confirmed by an analytical method based on the power series expansion of the
frequency in terms of the horizon radius. The same procedure applied to the
Schwarzschild anti-de Sitter spacetime proves that the purely damped frequency
goes as , where is the quantum number characterizing
the angular distribution. Finally, we study the limit of high overtones and
find that the frequencies become evenly spaced in this regime. The spacing of
the frequency per unit horizon radius seems to be a universal quantity, in the
sense that it is independent of the wave number, perturbation parity and black
hole size.Comment: Added new material on the asymptotic behavior of QNM
Quantum mechanical virial theorem in systems with translational and rotational symmetry
Generalized virial theorem for quantum mechanical nonrelativistic and
relativistic systems with translational and rotational symmetry is derived in
the form of the commutator between the generator of dilations G and the
Hamiltonian H. If the conditions of translational and rotational symmetry
together with the additional conditions of the theorem are satisfied, the
matrix elements of the commutator [G, H] are equal to zero on the subspace of
the Hilbert space. Normalized simultaneous eigenvectors of the particular set
of commuting operators which contains H, J^{2}, J_{z} and additional operators
form an orthonormal basis in this subspace. It is expected that the theorem is
relevant for a large number of quantum mechanical N-particle systems with
translational and rotational symmetry.Comment: 24 pages, accepted for publication in International Journal of
Theoretical Physic
Extracting spectral density function of a binary composite without a-priori assumption
The spectral representation separates the contributions of geometrical
arrangement (topology) and intrinsic constituent properties in a composite. The
aim of paper is to present a numerical algorithm based on the Monte Carlo
integration and contrainted-least-squares methods to resolve the spectral
density function for a given system. The numerical method is verified by
comparing the results with those of Maxwell-Garnett effective permittivity
expression. Later, it is applied to a well-studied rock-and-brine system to
instruct its utility. The presented method yields significant microstructural
information in improving our understanding how microstructure influences the
macroscopic behaviour of composites without any intricate mathematics.Comment: 4 pages, 5 figures and 1 tabl
On micro-structural effects in dielectric mixtures
The paper presents numerical simulations performed on dielectric properties
of two-dimensional binary composites on eleven regular space filling
tessellations. First, significant contributions of different parameters, which
play an important role in the electrical properties of the composite, are
introduced both for designing and analyzing material mixtures. Later, influence
of structural differences and intrinsic electrical properties of constituents
on the composite's over all electrical properties are investigated. The
structural differences are resolved by the spectral density representation
approach. The numerical technique, without any {\em a-priori} assumptions, for
extracting the spectral density function is also presented.Comment: 24 pages, 8 figure and 7 tables. It is submitted to IEEE Transactions
on Dielectrics and Electrical Insulatio