285 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.
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
Nutrition in agricultural development: The case of irrigated rice cultivation in West Kenya
ASC – Publicaties niet-programma gebonde
Temperature dependence of optical spectral weights in quarter-filled ladder systems
The temperature dependence of the integrated optical conductivity I(T)
reflects the changes of the kinetic energy as spin and charge correlations
develop. It provides a unique way to explore experimentally the kinetic
properties of strongly correlated systems. We calculated I(T) in the frame of a
t-J-V model at quarter-filling for ladder systems, like NaV_2O_5, and show that
the measured strong T dependence of I(T) for NaV_2O_5 can be explained by the
destruction of short range antiferromagnetic correlations. Thus I(T) provides
detailed information about super-exchange and magnetic energy scales.Comment: 4 pages, 5 figure
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