532 research outputs found
The Anderson model of localization: a challenge for modern eigenvalue methods
We present a comparative study of the application of modern eigenvalue
algorithms to an eigenvalue problem arising in quantum physics, namely, the
computation of a few interior eigenvalues and their associated eigenvectors for
the large, sparse, real, symmetric, and indefinite matrices of the Anderson
model of localization. We compare the Lanczos algorithm in the 1987
implementation of Cullum and Willoughby with the implicitly restarted Arnoldi
method coupled with polynomial and several shift-and-invert convergence
accelerators as well as with a sparse hybrid tridiagonalization method. We
demonstrate that for our problem the Lanczos implementation is faster and more
memory efficient than the other approaches. This seemingly innocuous problem
presents a major challenge for all modern eigenvalue algorithms.Comment: 16 LaTeX pages with 3 figures include
Decision-making in Swiss home-like childbirth: A grounded theory study
Background: Decision-making in midwifery, including a claim for shared decision-making between midwives and women, is of major significance for the health of mother and child. Midwives have little information about how to share decision-making responsibilities with women, especially when complications arise during birth.
Aim: To increase understanding of decision-making in complex home-like birth settings by exploring midwives’ and women’s perspectives and to develop a dynamic model integrating participatory processes for making shared decisions.
Methods: The study, based on grounded theory methodology, analysed 20 interviews of midwives and 20 women who had experienced complications in home-like births.
Findings: The central phenomenon that arose from the data was “defining/redefining decision as a joint commitment to healthy childbirth”. The sub-indicators that make up this phenomenon were safety, responsibility, mutual and personal commitments. These sub-indicators were also identified to influence temporal conditions of decision-making and to apply different strategies for shared decision-making. Women adopted strategies such as delegating a decision, making the midwife’s decision her own, challenging a decision or taking a decision driven by the dynamics of childbirth. Midwives employed strategies such as remaining indecisive, approving a woman’s decision, making an informed decision or taking the necessary decision.
Discussion and conclusion: To respond to recommendations for shared responsibility for care, midwives need to strengthen their shared decision-making skills. The visual model of decision-making in childbirth derived from the data provides a framework for transferring clinical reasoning into practice
The three-dimensional Anderson model of localization with binary random potential
We study the three-dimensional two-band Anderson model of localization and
compare our results to experimental results for amorphous metallic alloys
(AMA). Using the transfer-matrix method, we identify and characterize the
metal-insulator transitions as functions of Fermi level position, band
broadening due to disorder and concentration of alloy composition. The
appropriate phase diagrams of regions of extended and localized electronic
states are studied and qualitative agreement with AMA such as Ti-Ni and Ti-Cu
metallic glasses is found. We estimate the critical exponents nu_W, nu_E and
nu_x when either disorder W, energy E or concentration x is varied,
respectively. All our results are compatible with the universal value nu ~ 1.6
obtained in the single-band Anderson model.Comment: 9 RevTeX4 pages with 11 .eps figures included, submitted to PR
Energy-level statistics at the metal-insulator transition in anisotropic systems
We study the three-dimensional Anderson model of localization with
anisotropic hopping, i.e. weakly coupled chains and weakly coupled planes. In
our extensive numerical study we identify and characterize the metal-insulator
transition using energy-level statistics. The values of the critical disorder
are consistent with results of previous studies, including the
transfer-matrix method and multifractal analysis of the wave functions.
decreases from its isotropic value with a power law as a function of
anisotropy. Using high accuracy data for large system sizes we estimate the
critical exponent . This is in agreement with its value in the
isotropic case and in other models of the orthogonal universality class. The
critical level statistics which is independent of the system size at the
transition changes from its isotropic form towards the Poisson statistics with
increasing anisotropy.Comment: 22 pages, including 8 figures, revtex few typos corrected, added
journal referenc
Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis
We compare different partitioning schemes for the box-counting algorithm in
the multifractal analysis by computing the singularity spectrum and the
distribution of the box probabilities. As model system we use the Anderson
model of localization in two and three dimensions. We show that a partitioning
scheme which includes unrestricted values of the box size and an average over
all box origins leads to smaller error bounds than the standard method using
only integer ratios of the linear system size and the box size which was found
by Rodriguez et al. (Eur. Phys. J. B 67, 77-82 (2009)) to yield the most
reliable results.Comment: 10 pages, 13 figure
Multifractal analysis of the metal-insulator transition in anisotropic systems
We study the Anderson model of localization with anisotropic hopping in three
dimensions for weakly coupled chains and weakly coupled planes. The eigenstates
of the Hamiltonian, as computed by Lanczos diagonalization for systems of sizes
up to , show multifractal behavior at the metal-insulator transition even
for strong anisotropy. The critical disorder strength determined from the
system size dependence of the singularity spectra is in a reasonable agreement
with a recent study using transfer matrix methods. But the respective spectrum
at deviates from the ``characteristic spectrum'' determined for the
isotropic system. This indicates a quantitative difference of the multifractal
properties of states of the anisotropic as compared to the isotropic system.
Further, we calculate the Kubo conductivity for given anisotropies by exact
diagonalization. Already for small system sizes of only sites we observe
a rapidly decreasing conductivity in the directions with reduced hopping if the
coupling becomes weaker.Comment: 25 RevTeX pages with 10 PS-figures include
Numerical verification of universality for the Anderson transition
We analyze the scaling behavior of the higher Lyapunov exponents at the
Anderson transition. We estimate the critical exponent and verify its
universality and that of the critical conductance distribution for box,
Gaussian and Lorentzian distributions of the random potential
Effects of Scale-Free Disorder on the Anderson Metal-Insulator Transition
We investigate the three-dimensional Anderson model of localization via a
modified transfer-matrix method in the presence of scale-free diagonal disorder
characterized by a disorder correlation function decaying asymptotically
as . We study the dependence of the localization-length exponent
on the correlation-strength exponent . % For fixed disorder ,
there is a critical , such that for ,
and for , remains that of the
uncorrelated system in accordance with the extended Harris criterion. At the
band center, is independent of but equal to that of the
uncorrelated system. The physical mechanisms leading to this different behavior
are discussed.Comment: submitted to Phys. Rev. Let
Metal-insulator transitions in anisotropic 2d systems
Several phenomena related to the critical behaviour of non-interacting
electrons in a disordered 2d tight-binding system with a magnetic field are
studied. Localization lengths, critical exponents and density of states are
computed using transfer matrix techniques. Scaling functions of isotropic
systems are recovered once the dimension of the system in each direction is
chosen proportional to the localization length. It is also found that the
critical point is independent of the propagation direction, and that the
critical exponents for the localization length for both propagating directions
are equal to that of the isotropic system (approximately 7/3). We also
calculate the critical value of the scaling function for both the isotropic and
the anisotropic system. It is found that the isotropic value equals the
geometric mean of the two anisotropic values. Detailed numerical studies of the
density of states for the isotropic system reveals that for an appreciable
amount of disorder the critical energy is off the band center.Comment: 6 pages RevTeX, 6 figures included, submitted to Physical Review
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