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Number of Pages: 17Integrative BiologyGeological Science
Optimal Correlation Estimators for Quantized Signals
Using a maximum-likelihood criterion, we derive optimal correlation
strategies for signals with and without digitization. We assume that the
signals are drawn from zero-mean Gaussian distributions, as is expected in
radio-astronomical applications, and we present correlation estimators both
with and without a priori knowledge of the signal variances. We demonstrate
that traditional estimators of correlation, which rely on averaging products,
exhibit large and paradoxical noise when the correlation is strong. However, we
also show that these estimators are fully optimal in the limit of vanishing
correlation. We calculate the bias and noise in each of these estimators and
discuss their suitability for implementation in modern digital correlators.Comment: 8 Pages, 3 Figures, Submitted to Ap
Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
In a recent paper Bender and Mannheim showed that the unequal-frequency
fourth-order derivative Pais-Uhlenbeck oscillator model has a realization in
which the energy eigenvalues are real and bounded below, the Hilbert-space
inner product is positive definite, and time evolution is unitary. Central to
that analysis was the recognition that the Hamiltonian of the
model is PT symmetric. This Hamiltonian was mapped to a conventional
Dirac-Hermitian Hamiltonian via a similarity transformation whose form was
found exactly. The present paper explores the equal-frequency limit of the same
model. It is shown that in this limit the similarity transform that was used
for the unequal-frequency case becomes singular and that becomes a
Jordan-block operator, which is nondiagonalizable and has fewer energy
eigenstates than eigenvalues. Such a Hamiltonian has no Hermitian counterpart.
Thus, the equal-frequency PT theory emerges as a distinct realization of
quantum mechanics. The quantum mechanics associated with this Jordan-block
Hamiltonian can be treated exactly. It is shown that the Hilbert space is
complete with a set of nonstationary solutions to the Schr\"odinger equation
replacing the missing stationary ones. These nonstationary states are needed to
establish that the Jordan-block Hamiltonian of the equal-frequency
Pais-Uhlenbeck model generates unitary time evolution.Comment: 39 pages, 0 figure
Transmission and Reflection in the Stadium Billiard: Time-dependent asymmetric transport
We investigate the transmission and reflection survival probabilities for the
chaotic stadium billiard with two holes placed asymmetrically. Classically,
these distributions are shown to have algebraic or exponential decays depending
on the choice of injecting hole and exact expressions are given for the first
time and confirmed numerically. As there is no reported quantum theoretical or
experimental analogue we propose a model for experimental observation of the
asymmetric transport using semiconductor nano-structures and comment on the
relevant quantum time-scales.Comment: 4 pages, 4 figure
Perturbation theory of the mass enhancement for a polaron coupled to acoustic phonons
We use both a perturbative Green's function analysis and standard
perturbative quantum mechanics to calculate the decrease in energy and the
effective mass for an electron interacting with acoustic phonons. The
interaction is between the difference in lattice displacements for neighbouring
ions, and the hopping amplitude for an electron between those two sites. The
calculations are performed in one, two, and three dimensions, and comparisons
are made with results from other electron-phonon models. We also compute the
spectral function and quasiparticle residue, as a function of characteristic
phonon frequency. There are strong indications that this model is always
polaronic on one dimension, where an unusual relation between the effective
mass and the quasiparticle residue is also found.Comment: 9 pages, 5 figures, submitted to PR
Developing And Delivering The Virtual MBA Course
The use of the Internet offers a unique opportunity to bring together individuals in an interactive setting for social and educational purposes. Colleges and universities have augmented their brick and mortar classes with virtual course offerings using the Internet for distance education. This paper will examine the origins of distance education and offer insights and recommendations for developing and delivering an on-line MBA course in Privacy and Information Security
Hard Discs on the Hyperbolic Plane
We examine a simple hard disc fluid with no long range interactions on the
two dimensional space of constant negative Gaussian curvature, the hyperbolic
plane. This geometry provides a natural mechanism by which global crystalline
order is frustrated, allowing us to construct a tractable model of disordered
monodisperse hard discs. We extend free area theory and the virial expansion to
this regime, deriving the equation of state for the system, and compare its
predictions with simulation near an isostatic packing in the curved space.Comment: 4 pages, 3 figures, included, final versio
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