691 research outputs found
Tagged particle process in continuum with singular interactions
By using Dirichlet form techniques we construct the dynamics of a tagged
particle in an infinite particle environment of interacting particles for a
large class of interaction potentials. In particular, we can treat interaction
potentials having a singularity at the origin, non-trivial negative part and
infinite range, as e.g., the Lennard-Jones potential.Comment: 27 pages, proof for conservativity added, tightened presentatio
Spherical codes, maximal local packing density, and the golden ratio
The densest local packing (DLP) problem in d-dimensional Euclidean space Rd
involves the placement of N nonoverlapping spheres of unit diameter near an
additional fixed unit-diameter sphere such that the greatest distance from the
center of the fixed sphere to the centers of any of the N surrounding spheres
is minimized. Solutions to the DLP problem are relevant to the realizability of
pair correlation functions for packings of nonoverlapping spheres and might
prove useful in improving upon the best known upper bounds on the maximum
packing fraction of sphere packings in dimensions greater than three. The
optimal spherical code problem in Rd involves the placement of the centers of N
nonoverlapping spheres of unit diameter onto the surface of a sphere of radius
R such that R is minimized. It is proved that in any dimension, all solutions
between unity and the golden ratio to the optimal spherical code problem for N
spheres are also solutions to the corresponding DLP problem. It follows that
for any packing of nonoverlapping spheres of unit diameter, a spherical region
of radius less than or equal to the golden ratio centered on an arbitrary
sphere center cannot enclose a number of sphere centers greater than one more
than the number that can be placed on the region's surface.Comment: 12 pages, 1 figure. Accepted for publication in the Journal of
Mathematical Physic
Universal correlations of trapped one-dimensional impenetrable bosons
We calculate the asymptotic behaviour of the one body density matrix of
one-dimensional impenetrable bosons in finite size geometries. Our approach is
based on a modification of the Replica Method from the theory of disordered
systems. We obtain explicit expressions for oscillating terms, similar to
fermionic Friedel oscillations. These terms are universal and originate from
the strong short-range correlations between bosons in one dimension.Comment: 18 pages, 3 figures. Published versio
Markov evolutions and hierarchical equations in the continuum I. One-component systems
General birth-and-death as well as hopping stochastic dynamics of infinite
particle systems in the continuum are considered. We derive corresponding
evolution equations for correlation functions and generating functionals.
General considerations are illustrated in a number of concrete examples of
Markov evolutions appearing in applications.Comment: 47 page
Gravitational lensing: a unique probe of dark matter and dark energy
I review the development of gravitational lensing as a powerful tool of the observational cosmologist. After the historic eclipse expedition organized by Arthur Eddington and Frank Dyson, the subject lay observationally dormant for 60 years. However, subsequent progress has been astonishingly rapid, especially in the past decade, so that gravitational lensing now holds the key to unravelling the two most profound mysteries of our Universeâthe nature and distribution of dark matter, and the origin of the puzzling cosmic acceleration first identified in the late 1990s. In this non-specialist review, I focus on the unusual history and achievements of gravitational lensing and its future observational prospects
One-dimensional classical adjoint SU(2) Coulomb Gas
The equation of state of a one-dimensional classical nonrelativistic Coulomb
gas of particles in the adjoint representation of SU(2) is given. The problem
is solved both with and without sources in the fundamental representation at
either end of the system. The gas exhibits confining properties at low
densities and temperatures and deconfinement in the limit of high densities and
temperatures. However, there is no phase transition to a regime where the
string tension vanishes identically; true deconfinement only happens for
infinite densities and temperatures. In the low density, low temperature limit,
a new type of collective behavior is observed.Comment: 6 pages, 1 postscript figur
Longitudinal patterns in an Arkansas River Valley stream: an Application of the River Continuum Concept
The River Continuum Concept (RCC) provides the framework for studying how lotic ecosystems vary from headwater streams to large rivers. The RCC was developed in streams in eastern deciduous forests of North America, but watershed characteristics and land uses differ across ecoregions, presenting unique opportunities to study how predictions of the RCC may differ across regions. Additionally, RCC predictions may vary due to the influence of fishes, but few studies have used fish taxa as a metric for evaluating predictions of the RCC. Our goal was to determine if RCC predictions for stream orders 1 through 5 were supported by primary producer, macroinvertebrate, and fish communities in Cadron Creek of the Arkansas River Valley. We sampled chlorophyll a, macroinvertebrates, and fishes at five stream reaches across a gradient of watershed size. Contrary to RCC predictions, chlorophyll a did not increase in concentration with catchment size. As the RCC predicts, fish and macroinvertebrate diversity increased with catchment size. Shredding and collecting macroinvertebrate taxa supported RCC predictions, respectively decreasing and increasing in composition as catchment area increased. Herbivorous and predaceous fish did not follow RCC predictions; however, surface-water column feeding fish were abundant at all sites as predicted. We hypothesize some predictions of the RCC were not supported in headwater reaches of this system due to regional differences in watershed characteristics and altered resource availability due to land use surrounding sampling sites
Three-coloring statistical model with domain wall boundary conditions. I. Functional equations
In 1970 Baxter considered the statistical three-coloring lattice model for
the case of toroidal boundary conditions. He used the Bethe ansatz and found
the partition function of the model in the thermodynamic limit. We consider the
same model but use other boundary conditions for which one can prove that the
partition function satisfies some functional equations similar to the
functional equations satisfied by the partition function of the six-vertex
model for a special value of the crossing parameter.Comment: 16 pages, notations changed for consistency with the next part,
appendix adde
Correlation functions and momentum distribution of one-dimensional Bose systems
The ground-state correlation properties of a one-dimensional Bose system
described by the Lieb-Liniger Hamiltonian are investigated by using exact
quantum Monte Carlo techniques. The pair distribution function, static
structure factor, one-body density matrix and momentum distribution of a
homogeneous system are calculated for different values of the gas parameter
ranging from the Tonks-Girardeau to the mean-field regime. Results for the
momentum distribution of a harmonically trapped gas in configurations relevant
to experiments are also presented.Comment: 4 pages, 5 figure
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