8,898 research outputs found
An analysis of the noise reduction of orthotropic cylindrical shells Final report
Statistical energy and classical methods for calculating noise reduction of orthotropic cylindrical shell
Observation of PT phase transition in a simple mechanical system
If a Hamiltonian is PT symmetric, there are two possibilities: Either the
eigenvalues are entirely real, in which case the Hamiltonian is said to be in
an unbroken-PT-symmetric phase, or else the eigenvalues are partly real and
partly complex, in which case the Hamiltonian is said to be in a
broken-PT-symmetric phase. As one varies the parameters of the Hamiltonian, one
can pass through the phase transition that separates the unbroken and broken
phases. This transition has recently been observed in a variety of laboratory
experiments. This paper explains the phase transition in a simple and intuitive
fashion and then describes an extremely elementary experiment in which the
phase transition is easily observed.Comment: 9 pages, 9 figure
Asymptotic Analysis of the Boltzmann Equation for Dark Matter Relics
This paper presents an asymptotic analysis of the Boltzmann equations
(Riccati differential equations) that describe the physics of thermal
dark-matter-relic abundances. Two different asymptotic techniques are used,
boundary-layer theory, which makes use of asymptotic matching, and the delta
expansion, which is a powerful technique for solving nonlinear differential
equations. Two different Boltzmann equations are considered. The first is
derived from general relativistic considerations and the second arises in
dilatonic string cosmology. The global asymptotic analysis presented here is
used to find the long-time behavior of the solutions to these equations. In the
first case the nature of the so-called freeze-out region and the
post-freeze-out behavior is explored. In the second case the effect of the
dilaton on cold dark-matter abundances is calculated and it is shown that there
is a large-time power-law fall off of the dark-matter abundance. Corrections to
the power-law behavior are also calculated.Comment: 15 pages, no figure
On the eigenproblems of PT-symmetric oscillators
We consider the non-Hermitian Hamiltonian H=
-\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a
polynomial of degree at most n \geq 1 with all nonnegative real coefficients
(possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the
sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case
H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the
eigenfunction u and its derivative u^\prime and we find some other interesting
properties of eigenfunctions.Comment: 21pages, 9 figure
A perturbative approach to the spectral zeta functions of strings, drums and quantum billiards
We have obtained an explicit expression for the spectral zeta functions and
for the heat kernel of strings, drums and quantum billiards working to third
order in perturbation theory, using a generalization of the binomial theorem to
operators. The perturbative parameter used in the expansion is either the small
deformation of a reference domain (for instance a square), or a small variation
of the density around a constant value (in two dimensions both cases can
apply). This expansion is well defined even in presence of degenerations of the
unperturbed spectrum. We have discussed several examples in one, two and three
dimensions, obtaining in some cases the analytic continuation of the series,
which we have then used to evaluate the corresponding Casimir energy. For the
case of a string with piecewise constant density, subject to different boundary
conditions, and of two concentric cylinders of very close radii, we have
reproduced results previously published, thus obtaining a useful check of our
method.Comment: 23 pages, 5 figures, 2 tables; version accepted on Journal of
Mathematical Physic
Regularization of second-order scalar perturbation produced by a point-particle with a nonlinear coupling
Accurate calculation of the motion of a compact object in a background
spacetime induced by a supermassive black hole is required for the future
detection of such binary systems by the gravitational-wave detector LISA.
Reaching the desired accuracy requires calculation of the second-order
gravitational perturbations produced by the compact object. At the point
particle limit the second-order gravitational perturbation equations turn out
to have highly singular source terms, for which the standard retarded solutions
diverge. Here we study a simplified scalar toy-model in which a point particle
induces a nonlinear scalar field in a given curved spacetime. The corresponding
second-order scalar perturbation equation in this model is found to have a
similar singular source term, and therefore its standard retarded solutions
diverge. We develop a regularization method for constructing well-defined
causal solutions for this equation. Notably these solutions differ from the
standard retarded solutions, which are ill-defined in this case.Comment: 14 page
Searching for Massive Black Hole Binaries in the first Mock LISA Data Challenge
The Mock LISA Data Challenge is a worldwide effort to solve the LISA data
analysis problem. We present here our results for the Massive Black Hole Binary
(BBH) section of Round 1. Our results cover Challenge 1.2.1, where the
coalescence of the binary is seen, and Challenge 1.2.2, where the coalescence
occurs after the simulated observational period. The data stream is composed of
Gaussian instrumental noise plus an unknown BBH waveform. Our search algorithm
is based on a variant of the Markov Chain Monte Carlo method that uses
Metropolis-Hastings sampling and thermostated frequency annealing. We present
results from the training data sets and the blind data sets. We demonstrate
that our algorithm is able to rapidly locate the sources, accurately recover
the source parameters, and provide error estimates for the recovered
parameters.Comment: 11 pages, 6 figures, Submitted to CQG proceedings of GWDAW 11, AEI,
Germany, Dec 200
sd-shell study with a multi-configuration mixing approach designed for large scale nuclear structure calculations
A systematic numerical investigation of a recently developed nuclear structure approach is presented which diagonalizes the Hamiltonian in the space of the symmetry-projected Hartree-Fock-Bogoliubov (HFB) vacuum and symmetry-projected quasiparticle excitations with respect to it. The underlying HFB transformation, which is assumed to be time-reversal and axially symmetric, is determined by variation after the projection. The model allows the use of large basis systems. It has been applied to the calculation of energy spectra of several even-even, odd-odd and odd mass nuclei in the sd shell with mass numbers reaching from A=20 to 30. The Chung-Wildenthal interaction has been used. Good agreement with the exact shell model diagonalization and a considerable improvement on a previous approach, where the HFB transformation was significantly more restricted, is obtained
Use of Equivalent Hermitian Hamiltonian for -Symmetric Sinusoidal Optical Lattices
We show how the band structure and beam dynamics of non-Hermitian
-symmetric sinusoidal optical lattices can be approached from the point of
view of the equivalent Hermitian problem, obtained by an analytic continuation
in the transverse spatial variable . In this latter problem the eigenvalue
equation reduces to the Mathieu equation, whose eigenfunctions and properties
have been well studied. That being the case, the beam propagation, which
parallels the time-development of the wave-function in quantum mechanics, can
be calculated using the equivalent of the method of stationary states. We also
discuss a model potential that interpolates between a sinusoidal and periodic
square well potential, showing that some of the striking properties of the
sinusoidal potential, in particular birefringence, become much less prominent
as one goes away from the sinusoidal case.Comment: 11 pages, 8 figure
Pistons modeled by potentials
In this article we consider a piston modelled by a potential in the presence
of extra dimensions. We analyze the functional determinant and the Casimir
effect for this configuration. In order to compute the determinant and Casimir
force we employ the zeta function scheme. Essentially, the computation reduces
to the analysis of the zeta function associated with a scalar field living on
an interval in a background potential. Although, as a model for a
piston, it seems reasonable to assume a potential having compact support within
, we provide a formalism that can be applied to any sufficiently smooth
potential.Comment: 10 pages, LaTeX. A typo in eq. (3.5) has been corrected. In
"Cosmology, Quantum Vacuum and Zeta Functions: In Honour of Emilio Elizalde",
Eds. S.D. Odintsov, D. Saez-Gomez, and S. Xambo-Descamps. (Springer 2011) pp
31
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