15,999 research outputs found
Legendre transformations on the triangular lattice
The main purpose of the paper is to demonstrate that condition of invariance
with respect to the Legendre transformations allows effectively isolate the
class of integrable difference equations on the triangular lattice, which can
be considered as discrete analogues of relativistic Toda type lattices. Some of
obtained equations are new, up to the author knowledge. As an example, one of
them is studied in more details, in particular, its higher continuous
symmetries and zero curvature representation are found.Comment: 13 pages, late
Convex Dynamics and Applications
This paper proves a theorem about bounding orbits of a time dependent
dynamical system. The maps that are involved are examples in convex dynamics,
by which we mean the dynamics of piecewise isometries where the pieces are
convex. The theorem came to the attention of the authors in connection with the
problem of digital halftoning. \textit{Digital halftoning} is a family of
printing technologies for getting full color images from only a few different
colors deposited at dots all of the same size. The simplest version consist in
obtaining grey scale images from only black and white dots. A corollary of the
theorem is that for \textit{error diffusion}, one of the methods of digital
halftoning, averages of colors of the printed dots converge to averages of the
colors taken from the same dots of the actual images. Digital printing is a
special case of a much wider class of scheduling problems to which the theorem
applies. Convex dynamics has roots in classical areas of mathematics such as
symbolic dynamics, Diophantine approximation, and the theory of uniform
distributions.Comment: LaTex with 9 PostScript figure
Dressing chain for the acoustic spectral problem
The iterations are studied of the Darboux transformation for the generalized
Schroedinger operator. The applications to the Dym and Camassa-Holm equations
are considered.Comment: 16 pages, 6 eps figure
Types of quantum information
Quantum, in contrast to classical, information theory, allows for different
incompatible types (or species) of information which cannot be combined with
each other. Distinguishing these incompatible types is useful in understanding
the role of the two classical bits in teleportation (or one bit in one-bit
teleportation), for discussing decoherence in information-theoretic terms, and
for giving a proper definition, in quantum terms, of ``classical information.''
Various examples (some updating earlier work) are given of theorems which
relate different incompatible kinds of information, and thus have no
counterparts in classical information theory.Comment: Minor changes so as to agree with published versio
A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula
Continuing our development of a mathematical theory of stochastic
microlensing, we study the random shear and expected number of random lensed
images of different types. In particular, we characterize the first three
leading terms in the asymptotic expression of the joint probability density
function (p.d.f.) of the random shear tensor at a general point in the lens
plane due to point masses in the limit of an infinite number of stars. Up to
this order, the p.d.f. depends on the magnitude of the shear tensor, the
optical depth, and the mean number of stars through a combination of radial
position and the stars' masses. As a consequence, the p.d.f.s of the shear
components are seen to converge, in the limit of an infinite number of stars,
to shifted Cauchy distributions, which shows that the shear components have
heavy tails in that limit. The asymptotic p.d.f. of the shear magnitude in the
limit of an infinite number of stars is also presented. Extending to general
random distributions of the lenses, we employ the Kac-Rice formula and Morse
theory to deduce general formulas for the expected total number of images and
the expected number of saddle images. We further generalize these results by
considering random sources defined on a countable compact covering of the light
source plane. This is done to introduce the notion of {\it global} expected
number of positive parity images due to a general lensing map. Applying the
result to microlensing, we calculate the asymptotic global expected number of
minimum images in the limit of an infinite number of stars, where the stars are
uniformly distributed. This global expectation is bounded, while the global
expected number of images and the global expected number of saddle images
diverge as the order of the number of stars.Comment: To appear in JM
Path Integral Monte Carlo study of phonons in the bcc phase of He
Using Path Integral Monte Carlo and the Maximum Entropy method, we calculate
the dynamic structure factor of solid He in the bcc phase at a finite
temperature of T = 1.6 K and a molar volume of 21 cm. Both the
single-phonon contribution to the dynamic structure factor and the total
dynamic structure factor are evaluated. From the dynamic structure factor, we
obtain the phonon dispersion relations along the main crystalline directions,
[001], [011] and [111]. We calculate both the longitudinal and transverse
phonon branches. For the latter, no previous simulations exist. We discuss the
differences between dispersion relations resulting from the single-phonon part
vs. the total dynamic structure factor. In addition, we evaluate the formation
energy of a vacancy.Comment: 10 figure
Coupling efficiency for phase locking of a spin transfer oscillator to a microwave current
The phase locking behavior of spin transfer nano-oscillators (STNOs) to an
external microwave signal is experimentally studied as a function of the STNO
intrinsic parameters. We extract the coupling strength from our data using the
derived phase dynamics of a forced STNO. The predicted trends on the coupling
strength for phase locking as a function of intrinsic features of the
oscillators i.e. power, linewidth, agility in current, are central to optimize
the emitted power in arrays of mutually coupled STNOs
Expansion for -Core Percolation
The physics of -core percolation pertains to those systems whose
constituents require a minimum number of connections to each other in order
to participate in any clustering phenomenon. Examples of such a phenomenon
range from orientational ordering in solid ortho-para mixtures to
the onset of rigidity in bar-joint networks to dynamical arrest in
glass-forming liquids. Unlike ordinary () and biconnected ()
percolation, the mean field -core percolation transition is both
continuous and discontinuous, i.e. there is a jump in the order parameter
accompanied with a diverging length scale. To determine whether or not this
hybrid transition survives in finite dimensions, we present a expansion
for -core percolation on the -dimensional hypercubic lattice. We show
that to order the singularity in the order parameter and in the
susceptibility occur at the same value of the occupation probability. This
result suggests that the unusual hybrid nature of the mean field -core
transition survives in high dimensions.Comment: 47 pages, 26 figures, revtex
Are Massive Elementary Particles Black Holes?
We use exact results in a new approach to quantum gravity to study the effect
of quantum loop corrections on the behavior of the metric of space-time near
the Schwarzschild radius of a massive point particle in the Standard Model. We
show that the classical conclusion that such a system is a black hole is
obviated. Phenomenological implications are discussed.Comment: 9 pages, 1 figure; improved tex
Quantum Corrections to Newton's Law in Resummed Quantum Gravity
We present the elements of resummed quantum gravity, a new approach to
quantum gravity based on the work of Feynman using the simplest example of a
scalar field as the representative matter. We show that we get a UV finite
quantum correction to Newton's law.Comment: 4 pages, 1 figure; presented by B.F.L. Ward at DPF200
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