340 research outputs found
Random Walkers with Shrinking Steps in d-Dimensions and Their Long Term Memory
We study, in d-dimensions, the random walker with geometrically shrinking
step sizes at each hop. We emphasize the integrated quantities such as
expectation values, cumulants and moments rather than a direct study of the
probability distribution. We develop a 1/d expansion technique and study
various correlations of the first step to the position as ti me goes to
infinity. We also show and substantiate with a study of the cumulants that to
order 1/d the system admits a continuum counterpart equation which can be
obtained with a generalization of the ordinary technique to obtain the
continuum limit. We also advocate that this continuum counterpart equation,
which is nothing but the ordinary diffusion equation with a diffusion constant
decaying exponentially in continuous time, captures all the qualitative aspects
of t he discrete system and is often a good starting point for quantitative
approximations
Non-universal behavior for aperiodic interactions within a mean-field approximation
We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit,
with the interaction constants following two deterministic aperiodic sequences:
Fibonacci or period-doubling ones. New algorithms of sequence generation were
implemented, which were fundamental in obtaining long sequences and, therefore,
precise results. We calculate the exact critical temperature for both
sequences, as well as the critical exponent , and . For
the Fibonacci sequence, the exponents are classical, while for the
period-doubling one they depend on the ratio between the two exchange
constants. The usual relations between critical exponents are satisfied, within
error bars, for the period-doubling sequence. Therefore, we show that
mean-field-like procedures may lead to nonclassical critical exponents.Comment: 6 pages, 7 figures, to be published in Phys. Rev.
High temperature thermal conductivity of 2-leg spin-1/2 ladders
Based on numerical simulations, a study of the high temperature, finite
frequency, thermal conductivity of spin-1/2 ladders is
presented. The exact diagonalization and a novel Lanczos technique are
employed.The conductivity spectra, analyzed as a function of rung coupling,
point to a non-diverging limit but to an unconventional low frequency
behavior. The results are discussed with perspective recent experiments
indicating a significant magnetic contribution to the energy transport in
quasi-one dimensional compounds.Comment: 4 pages, 4 figure
On general relation between quantum ergodicity and fidelity of quantum dynamics
General relation is derived which expresses the fidelity of quantum dynamics,
measuring the stability of time evolution to small static variation in the
hamiltonian, in terms of ergodicity of an observable generating the
perturbation as defined by its time correlation function. Fidelity for ergodic
dynamics is predicted to decay exponentially on time-scale proportional to
delta^(-2) where delta is the strength of perturbation, whereas faster,
typically gaussian decay on shorter time scale proportional to delta^(-1) is
predicted for integrable, or generally non-ergodic dynamics. This surprising
result is demonstrated in quantum Ising spin-1/2 chain periodically kicked with
a tilted magnetic field where we find finite parameter-space regions of
non-ergodic and non-integrable motion in thermodynamic limit.Comment: Slightly revised version, 4.5 RevTeX pages, 2 figure
Seasonality in the coastal lowlands of Kenya: Part 1: Research objectives and study design
This is the first of a number of reports on social, economic and nutritional conditions in Kwale and Kilifi Districts, Coast Province, Kenya. The reports deal in particular with regional and seasonal fluctuations in food supply and nutrition. This part contains a description of the research objectives and methodology.ASC – Publicaties niet-programma gebonde
Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations
Monte Carlo simulations and finite-size scaling analysis have been carried
out to study the critical behavior in a two-dimensional system of particles
with two bonding sites that, by decreasing temperature or increasing density,
polymerize reversibly into chains with discrete orientational degrees of
freedom and, at the same time, undergo a continuous isotropic-nematic (IN)
transition. A complete phase diagram was obtained as a function of temperature
and density. The numerical results were compared with mean field (MF) and real
space renormalization group (RSRG) analytical predictions about the IN
transformation. While the RSRG approach supports the continuous nature of the
transition, the MF solution predicts a first-order transition line and a
tricritical point, at variance with the simulation results.Comment: 12 pages, 10 figures, supplementary informatio
The anisotropic XY model on the inhomogeneous periodic chain
The static and dynamic properties of the anisotropic XY-model on
the inhomogeneous periodic chain, composed of cells with different
exchange interactions and magnetic moments, in a transverse field are
determined exactly at arbitrary temperatures. The properties are obtained by
introducing the Jordan-Wigner fermionization and by reducing the problem to a
diagonalization of a finite matrix of order. The quantum transitions are
determined exactly by analyzing, as a function of the field, the induced
magnetization 1/n\sum_{m=1}^{n}\mu_{m}\left ( denotes
the cell, the site within the cell, the magnetic moment at site
within the cell) and the spontaneous magnetization which is obtained from the correlations for large spin separations. These results,
which are obtained for infinite chains, correspond to an extension of the ones
obtained by Tong and Zhong(\textit{Physica B} \textbf{304,}91 (2001)). The
dynamic correlations, , and the dynamic
susceptibility, are also obtained at arbitrary
temperatures. Explicit results are presented in the limit T=0, where the
critical behaviour occurs, for the static susceptibility as
a function of the transverse field , and for the frequency dependency of
dynamic susceptibility .Comment: 33 pages, 13 figures, 01 table. Revised version (minor corrections)
accepted for publiction in Phys. Rev.
Dynamical Correlation Functions for One-Dimensional Quantum Spin Systems: New Results Based on a Rigorous Approach
We present new results on the time‐dependent correlation functions Ξ n (t) =4〈S ξ 0(t)S ξ n 〉, ξ=x,y at zero temperature of the one‐dimensional S=1/2 isotropic X Y model (h=γ=0) and of the transverse Ising model (TI) at the critical magnetic field (h=γ=1). Both models are characterized by special cases of the Hamiltonian H=−J∑ l [(1+γ)S x l S x l+1 +(1−γ)S y l S y l+1 +h S z l ]. We have derived exact results on the long‐time asymptotic expansions of the autocorrelation functions (ACF’s) Ξ0(t) and on the singularities of their frequency‐dependent Fourier transforms Φξξ 0(ω). We have also determined the latter functions by high‐precision numerical calculations. The functions Φξξ 0(ω), ξ=x,y have singularities at the infinite sequence of frequencies ω=mω0, m=0, 1, 2, 3, ... where ω0=J for the X Y model and ω0=2J for the TI model. In both models the singularities in Φ x x 0 (ω) for m=0, 1 are divergent, whereas the nonanalyticities at higher frequencies become increasingly weaker. We point out that the nonanalyticities at ω≠0 are intrinsic features of the discrete quantum chain and have therefore not been found in the context of a continuum analysis
Dynamical structure factor of the anisotropic Heisenberg chain in a transverse field
We consider the anisotropic Heisenberg spin-1/2 chain in a transverse
magnetic field at zero temperature. We first determine all components of the
dynamical structure factor by combining exact results with a mean-field
approximation recently proposed by Dmitriev {\it et al}., JETP 95, 538 (2002).
We then turn to the small anisotropy limit, in which we use field theory
methods to obtain exact results. We discuss the relevance of our results to
Neutron scattering experiments on the 1D Heisenberg chain compound .Comment: 13 pages, 14 figure
On the segmentation and classification of hand radiographs
This research is part of a wider project to build predictive models of bone age using hand radiograph images. We examine ways of finding the outline of a hand from an X-ray as the first stage in segmenting the image into constituent bones. We assess a variety of algorithms including contouring, which has not previously been used in this context. We introduce a novel ensemble algorithm for combining outlines using two voting schemes, a likelihood ratio test and dynamic time warping (DTW). Our goal is to minimize the human intervention required, hence we investigate alternative ways of training a classifier to determine whether an outline is in fact correct or not. We evaluate outlining and classification on a set of 1370 images. We conclude that ensembling with DTW improves performance of all outlining algorithms, that the contouring algorithm used with the DTW ensemble performs the best of those assessed, and that the most effective classifier of hand outlines assessed is a random forest applied to outlines transformed into principal components
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