201 research outputs found
Search templates for stochastic gravitational-wave backgrounds
Several earth-based gravitational-wave (GW) detectors are actively pursuing
the quest for placing observational constraints on models that predict the
behavior of a variety of astrophysical and cosmological sources. These sources
span a wide gamut, ranging from hydrodynamic instabilities in neutron stars
(such as r-modes) to particle production in the early universe. Signals from a
subset of these sources are expected to appear in these detectors as stochastic
GW backgrounds (SGWBs). The detection of these backgrounds will help us in
characterizing their sources. Accounting for such a background will also be
required by some detectors, such as the proposed space-based detector LISA, so
that they can detect other GW signals. Here, we formulate the problem of
constructing a bank of search templates that discretely span the parameter
space of a generic SGWB. We apply it to the specific case of a class of
cosmological SGWBs, known as the broken power-law models. We derive how the
template density varies in their three-dimensional parameter space and show
that for the LIGO 4km detector pair, with LIGO-I sensitivities, about a few
hundred templates will suffice to detect such a background while incurring a
loss in signal-to-noise ratio of no more than 3%.Comment: Revtex, 7 pages, 18 eps figure
Possible way out of the Hawking paradox: Erasing the information at the horizon
We show that small deviations from spherical symmetry, described by means of
exact solutions to Einstein equations, provide a mechanism to "bleach" the
information about the collapsing body as it falls through the aparent horizon,
thereby resolving the information loss paradox. The resulting picture and its
implication related to the Landauer's principle in the presence of a
gravitational field, is discussed.Comment: 11 pages, Latex. Some comments added to answer to some raised
questions. Typos corected. Final version, to appear in Int. J. Modern. Phys.
Numerical approach to the Schrodinger equation in momentum space
The treatment of the time-independent Schrodinger equation in real-space is
an indispensable part of introductory quantum mechanics. In contrast, the
Schrodinger equation in momentum space is an integral equation that is not
readily amenable to an analytical solution and is rarely taught. We present a
numerical approach to the Schrodinger equation in momentum space. After a
suitable discretization process, we obtain the Hamiltonian matrix and
diagonalize it numerically. By considering a few examples, we show that this
approach is ideal for exploring bound-states in a localized potential and
complements the traditional (analytical or numerical) treatment of the
Schrodinger equation in real-space.Comment: 14 pages, 4 figures, several changes and one figure correctio
PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring
We study the properties of an N-site tight-binding ring with parity and
time-reversal (PT) symmetric, Hermitian, site-dependent tunneling and a pair of
non-Hermitian, PT-symmetric, loss and gain impurities . The
properties of such lattices with open boundary conditions have been intensely
explored over the past two years. We numerically investigate the PT-symmetric
phase in a ring with a position-dependent tunneling function
that, in an open lattice, leads to a
strengthened PT-symmetric phase, and study the evolution of the PT-symmetric
phase from the open chain to a ring. We show that, generally, periodic boundary
conditions weaken the PT-symmetric phase, although for experimentally relevant
lattice sizes , it remains easily accessible. We show that the
chirality, quantified by the (magnitude of the) average transverse momentum of
a wave packet, shows a maximum at the PT-symmetric threshold. Our results show
that although the wavepacket intensity increases monotonically across the
PT-breaking threshold, the average momentum decays monotonically on both sides
of the threshold.Comment: 11 pages, 5 figures, preprin
Dynamical eigenfunctions and critical density in loop quantum cosmology
We offer a new, physically transparent argument for the existence of the
critical, universal maximum matter density in loop quantum cosmology for the
case of a flat Friedmann-Lemaitre-Robertson-Walker cosmology with scalar
matter. The argument is based on the existence of a sharp exponential
ultraviolet cutoff in momentum space on the eigenfunctions of the quantum
cosmological dynamical evolution operator (the gravitational part of the
Hamiltonian constraint), attributable to the fundamental discreteness of
spatial volume in loop quantum cosmology. The existence of the cutoff is proved
directly from recently found exact solutions for the eigenfunctions for this
model. As a consequence, the operators corresponding to the momentum of the
scalar field and the spatial volume approximately commute. The ultraviolet
cutoff then implies that the scalar momentum, though not a bounded operator, is
in effect bounded on subspaces of constant volume, leading to the upper bound
on the expectation value of the matter density. The maximum matter density is
universal (i.e. independent of the quantum state) because of the linear scaling
of the cutoff with volume. These heuristic arguments are supplemented by a new
proof in the volume representation of the existence of the maximum matter
density. The techniques employed to demonstrate the existence of the cutoff
also allow us to extract the large volume limit of the exact eigenfunctions,
confirming earlier numerical and analytical work showing that the
eigenfunctions approach superpositions of the eigenfunctions of the
Wheeler-DeWitt quantization of the same model. We argue that generic (not just
semiclassical) quantum states approach symmetric superpositions of expanding
and contracting universes.Comment: 23 pages, 8 figures. Minor corrections throughout. Significant
improvement to key figure illustrating behavior of the eigenfunctions.
Version to appear in Classical and Quantum Gravit
Diffusion of particles in an expanding sphere with an absorbing boundary
We study the problem of particles undergoing Brownian motion in an expanding
sphere whose surface is an absorbing boundary for the particles. The problem is
akin to that of the diffusion of impurities in a grain of polycrystalline
material undergoing grain growth. We solve the time dependent diffusion
equation for particles in a d-dimensional expanding sphere to obtain the
particle density function (function of space and time). The survival rate or
the total number of particles per unit volume as a function of time is
evaluated. We have obtained particular solutions exactly for the case where d=3
and a parabolic growth of the sphere. Asymptotic solutions for the particle
density when the sphere growth rate is small relative to particle diffusivity
and vice versa are derived.Comment: 12 pages. To appear in J. Phys. A: Math. Theor. 41 (2008
Measuring longitudinal amplitudes for electroproduction of pseudoscalar mesons using recoil polarization in parallel kinematics
We propose a new method for measuring longitudinal amplitudes for
electroproduction of pseudoscalar mesons that exploits a symmetry relation for
polarization observables in parallel kinematics. This polarization technique
does not require variation of electron scattering kinematics and avoids the
major sources of systematic errors in Rosenbluth separation.Comment: intended for Phys. Rev. C as a Brief Repor
The Trigonometric Rosen-Morse Potential in the Supersymmetric Quantum Mechanics and its Exact Solutions
The analytic solutions of the one-dimensional Schroedinger equation for the
trigonometric Rosen-Morse potential reported in the literature rely upon the
Jacobi polynomials with complex indices and complex arguments. We first draw
attention to the fact that the complex Jacobi polynomials have non-trivial
orthogonality properties which make them uncomfortable for physics
applications. Instead we here solve above equation in terms of real orthogonal
polynomials. The new solutions are used in the construction of the
quantum-mechanic superpotential.Comment: 16 pages 7 figures 1 tabl
Non-Hermitian Rayleigh-Schroedinger Perturbation Theory
We devise a non-Hermitian Rayleigh-Schroedinger perturbation theory for the
single- and the multireference case to tackle both the many-body problem and
the decay problem encountered, for example, in the study of electronic
resonances in molecules. A complex absorbing potential (CAP) is employed to
facilitate a treatment of resonance states that is similar to the
well-established bound-state techniques. For the perturbative approach, the
full CAP-Schroedinger Hamiltonian, in suitable representation, is partitioned
according to the Epstein-Nesbet scheme. The equations we derive in the
framework of the single-reference perturbation theory turn out to be identical
to those obtained by a time-dependent treatment in Wigner-Weisskopf theory. The
multireference perturbation theory is studied for a model problem and is shown
to be an efficient and accurate method. Algorithmic aspects of the integration
of the perturbation theories into existing ab initio programs are discussed,
and the simplicity of their implementation is elucidated.Comment: 10 pages, 1 figure, RevTeX4, submitted to Physical Review
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