454 research outputs found
Green's function for a Schroedinger operator and some related summation formulas
Summation formulas are obtained for products of associated Lagurre
polynomials by means of the Green's function K for the Hamiltonian H =
-{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of
a Mercer type theorem that arises in connection with integral equations. The
new approach introduced in this paper may be useful for the construction of
wider classes of generating function.Comment: 14 page
Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators
We investigate the eigenvalues of perturbed spherical Schr\"odinger operators
under the assumption that the perturbation satisfies . We show that the square roots of eigenvalues are given by the square
roots of the unperturbed eigenvalues up to an decaying error depending on the
behavior of near . Furthermore, we provide sets of spectral data
which uniquely determine .Comment: 14 page
Relational time in generally covariant quantum systems: four models
We analize the relational quantum evolution of generally covariant systems in
terms of Rovelli's evolving constants of motion and the generalized Heisenberg
picture. In order to have a well defined evolution, and a consistent quantum
theory, evolving constants must be self-adjoint operators. We show that this
condition imposes strong restrictions to the choices of the clock variables. We
analize four cases. The first one is non- relativistic quantum mechanics in
parametrized form. We show that, for the free particle case, the standard
choice of time is the only one leading to self-adjoint evolving constants.
Secondly, we study the relativistic case. We show that the resulting quantum
theory is the free particle representation of the Klein Gordon equation in
which the position is a perfectly well defined quantum observable. The
admissible choices of clock variables are the ones leading to space-like
simultaneity surfaces. In order to mimic the structure of General Relativity we
study the SL(2R) model with two Hamiltonian constraints. The evolving constants
depend in this case on three independent variables. We show that it is possible
to find clock variables and inner products leading to a consistent quantum
theory. Finally, we discuss the quantization of a constrained model having a
compact constraint surface. All the models considered may be consistently
quantized, although some of them do not admit any time choice such that the
equal time surfaces are transversal to the orbits.Comment: 18 pages, revtex fil
Development of a Flow-Trough Microarray based Reverse Transcriptase Multiplex Ligation-Dependent Probe Amplification Assay for the Detection of European Bunyaviruses
It is suspected that apart from tick-borne encephalitis virus several additional European Arboviruses such as the sandfly borne Toscana virus, sandfly fever Sicilian virus and sandfly fever Naples virus, mosquito-borne Tahyna virus, Inkoo virus, Batai virus and tick-borne Uukuniemi virus cause aseptic meningo-encephalitis or febrile disease in Europe. Currently, the microarray technology is developing rapidly and there are many efforts to apply it to infectious diseases diagnostics. In order to arrive at an assay system useful for high throughput analysis of samples from aseptic meningo-encephalitis cases the authors developed a combined multiplex ligation-dependent probe amplification and flow-through microarray assay for the detection of European Bunyaviruses. These results show that this combined assay indeed is highly sensitive, and specific for the accurate detection of multiple viruses
Quantum Effects for the Dirac Field in Reissner-Nordstrom-AdS Black Hole Background
The behavior of a charged massive Dirac field on a Reissner-Nordstrom-AdS
black hole background is investigated. The essential self-adjointness of the
Dirac Hamiltonian is studied. Then, an analysis of the discharge problem is
carried out in analogy with the standard Reissner-Nordstrom black hole case.Comment: 18 pages, 5 figures, Iop styl
Absence of Normalizable Time-periodic Solutions for The Dirac Equation in Kerr-Newman-dS Black Hole Background
We consider the Dirac equation on the background of a Kerr-Newman-de Sitter
black hole. By performing variable separation, we show that there exists no
time-periodic and normalizable solution of the Dirac equation. This conclusion
holds true even in the extremal case. With respect to previously considered
cases, the novelty is represented by the presence, together with a black hole
event horizon, of a cosmological (non degenerate) event horizon, which is at
the root of the possibility to draw a conclusion on the aforementioned topic in
a straightforward way even in the extremal case.Comment: 12 pages. AMS styl
A Conformal Affine Toda Model of 2D-Black Holes the End-Point State and the S-Matrix
In this paper we investigate in more detail our previous formulation of the
dilaton-gravity theory by Bilal--Callan--de~Alwis as a -conformal affine
Toda (CAT) theory. Our main results are: i) a field redefinition of the
CAT-basis in terms of which it is possible to get the black hole solutions
already known in the literature; ii) an investigation the scattering matrix
problem for the quantum black hole states. It turns out that there is a range
of values of the free-falling shock matter fields forming the black hole
solution, in which the end-point state of the black hole evaporation is a zero
temperature regular remnant geometry. It seems that the quantum evolution to
this final state is non-unitary, in agreement with Hawking's scenario for the
black hole evaporation.Comment: ROM2F-93-03, 27 pages, phyzz
Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces
Reproducing kernel Hilbert spaces (RKHSs) play an important role in many
statistics and machine learning applications ranging from support vector
machines to Gaussian processes and kernel embeddings of distributions.
Operators acting on such spaces are, for instance, required to embed
conditional probability distributions in order to implement the kernel Bayes
rule and build sequential data models. It was recently shown that transfer
operators such as the Perron-Frobenius or Koopman operator can also be
approximated in a similar fashion using covariance and cross-covariance
operators and that eigenfunctions of these operators can be obtained by solving
associated matrix eigenvalue problems. The goal of this paper is to provide a
solid functional analytic foundation for the eigenvalue decomposition of RKHS
operators and to extend the approach to the singular value decomposition. The
results are illustrated with simple guiding examples
Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation
The Schroedinger equation on the half line is considered with a real-valued,
integrable potential having a finite first moment. It is shown that the
potential and the boundary conditions are uniquely determined by the data
containing the discrete eigenvalues for a boundary condition at the origin, the
continuous part of the spectral measure for that boundary condition, and a
subset of the discrete eigenvalues for a different boundary condition. This
result extends the celebrated two-spectrum uniqueness theorem of Borg and
Marchenko to the case where there is also a continuous spectru
Quantum harmonic oscillator systems with disorder
We study many-body properties of quantum harmonic oscillator lattices with
disorder. A sufficient condition for dynamical localization, expressed as a
zero-velocity Lieb-Robinson bound, is formulated in terms of the decay of the
eigenfunction correlators for an effective one-particle Hamiltonian. We show
how state-of-the-art techniques for proving Anderson localization can be used
to prove that these properties hold in a number of standard models. We also
derive bounds on the static and dynamic correlation functions at both zero and
positive temperature in terms of one-particle eigenfunction correlators. In
particular, we show that static correlations decay exponentially fast if the
corresponding effective one-particle Hamiltonian exhibits localization at low
energies, regardless of whether there is a gap in the spectrum above the ground
state or not. Our results apply to finite as well as to infinite oscillator
systems. The eigenfunction correlators that appear are more general than those
previously studied in the literature. In particular, we must allow for
functions of the Hamiltonian that have a singularity at the bottom of the
spectrum. We prove exponential bounds for such correlators for some of the
standard models
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