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 PTPT-Symmetric Sinusoidal Optical Lattices

We show how the band structure and beam dynamics of non-Hermitian $PT$-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 $x$. 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 $[0,L]$ in a background potential. Although, as a model for a piston, it seems reasonable to assume a potential having compact support within $[0,L]$, 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