196 research outputs found
The generalized localization lengths in one dimensional systems with correlated disorder
The scale invariant properties of wave functions in finite samples of one
dimensional random systems with correlated disorder are analyzed. The random
dimer model and its generalizations are considered and the wave functions are
compared. Generalized entropic localization lengths are introduced in order to
characterize the states and compared with their behavior for exponential
localization. An acceptable agreement is obtained, however, the exponential
form seems to be an oversimplification in the presence of correlated disorder.
According to our analysis in the case of the random dimer model and the two new
models the presence of power-law localization cannot be ruled out.Comment: 7 pages, LaTeX (IOP style), 2 figure
On Renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems
We discuss some properties of the generalized entropies, called Renyi
entropies and their application to the case of continuous distributions. In
particular it is shown that these measures of complexity can be divergent,
however, their differences are free from these divergences thus enabling them
to be good candidates for the description of the extension and the shape of
continuous distributions. We apply this formalism to the projection of wave
functions onto the coherent state basis, i.e. to the Husimi representation. We
also show how the localization properties of the Husimi distribution on average
can be reconstructed from its marginal distributions that are calculated in
position and momentum space in the case when the phase space has no structure,
i.e. no classical limit can be defined. Numerical simulations on a one
dimensional disordered system corroborate our expectations.Comment: 8 pages with 2 embedded eps figures, RevTex4, AmsMath included,
submitted to PR
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End-user interactions with intelligent and autonomous systems.
Systems that learn from or personalize themselves to users are quickly becoming mainstream yet interaction with these systems is limited and often uninformative for the end user. This workshop focuses on approaches and challenges to explore making these systems transparent, controllable and ultimately trustworthy to end users. The aims of the workshop are to help establish connections among researchers and industrial practitioners using real-world problems as catalysts to facilitate the exchange of approaches, solutions, and ideas about how to better support end users
Shape Analysis of the Level Spacing Distribution around the Metal Insulator Transition in the Three Dimensional Anderson Model
We present a new method for the numerical treatment of second order phase
transitions using the level spacing distribution function . We show that
the quantities introduced originally for the shape analysis of eigenvectors can
be properly applied for the description of the eigenvalues as well. The
position of the metal--insulator transition (MIT) of the three dimensional
Anderson model and the critical exponent are evaluated. The shape analysis of
obtained numerically shows that near the MIT is clearly different
from both the Brody distribution and from Izrailev's formula, and the best
description is of the form , with
. This is in good agreement with recent analytical results.Comment: 14 pages in plain TeX, 6 figures upon reques
Anomalously large critical regions in power-law random matrix ensembles
We investigate numerically the power-law random matrix ensembles.
Wavefunctions are fractal up to a characteristic length whose logarithm
diverges asymmetrically with different exponents, 1 in the localized phase and
0.5 in the extended phase. The characteristic length is so anomalously large
that for macroscopic samples there exists a finite critical region, in which
this length is larger than the system size. The Green's functions decrease with
distance as a power law with an exponent related to the correlation dimension.Comment: RevTex, 4 pages, 4 eps figures. Final version to be published in
Phys. Rev. Let
Comment on ``Critical Behavior in Disordered Quantum Systems Modified by Broken Time--Reversal Symmetry''
In a recent Letter [Phys. Rev. Lett. 80, 1003 (1998)] Hussein and Pato
employed the maximum entropy principle (MEP) in order to derive interpolating
ensembles between any pair of universality classes in random matrix theory.
They apply their formalism also to the transition from random matrix to Poisson
statistics of spectra that is observed for the case of the Anderson-type
metal-insulator transition. We point out the problems with the latter
procedure.Comment: 1 page in PS, to appear in PRL Sept. 2
Electron Correlation and the c-axis Dispersion of Cu d_z^2: a New Band Structure for High Temperature Superconductors
Previously we showed the major effect of electron correlation in the cuprate
superconductors is to lower the energy of the Cu d_x^2-y^2/O p_sigma (x^2-y^2)
band with respect to the Cu d_z^2/O' p_z (z^2) band. In our 2D Hubbard model
for La_1.85Sr_0.15CuO_4 (LaSCO), the z^2 band is narrow and crosses the
standard x^2-y^2 band just below the Fermi level. In this work, we introduce
c-axis dispersion to the model and find the z^2 band to have considerable
anisotropic 3D character. An additional hole-like surface opens up in the z^2
band at (0,0,2pi/c) which expands with doping. At sufficient doping levels, a
symmetry allowed x^2-y^2/z^2 band crossing along the (0,0)-(pi,pi) direction of
the Brillouin zone appears at the Fermi level. At this point, Cooper pairs
between the two bands (e.g. (k uparrow x^2-y^2/k downarrow z^2)) can form,
providing the basis for the Interband Pairing Theory of superconductivity in
these materials.Comment: submitted to Phys. Rev. Lett. Related publications: Phys. Rev. B 58,
12303 (1998); Phys. Rev. B 58, 12323 (1998); cond-mat/9903088;
cond-mat/990310
Configuration Complexities of Hydrogenic Atoms
The Fisher-Shannon and Cramer-Rao information measures, and the LMC-like or
shape complexity (i.e., the disequilibrium times the Shannon entropic power) of
hydrogenic stationary states are investigated in both position and momentum
spaces. First, it is shown that not only the Fisher information and the
variance (then, the Cramer-Rao measure) but also the disequilibrium associated
to the quantum-mechanical probability density can be explicitly expressed in
terms of the three quantum numbers (n, l, m) of the corresponding state.
Second, the three composite measures mentioned above are analytically,
numerically and physically discussed for both ground and excited states. It is
observed, in particular, that these configuration complexities do not depend on
the nuclear charge Z. Moreover, the Fisher-Shannon measure is shown to
quadratically depend on the principal quantum number n. Finally, sharp upper
bounds to the Fisher-Shannon measure and the shape complexity of a general
hydrogenic orbital are given in terms of the quantum numbers.Comment: 22 pages, 7 figures, accepted i
Classification of Polarimetric SAR Data Using Dictionary Learning
End-user development (EUD) research has yielded a variety of novel environments and techniques, often accompanied by lab-based usability studies that test their effectiveness in the completion of representative real-world tasks. While lab studies play an important role in resolving frustrations and demonstrating the potential of novel tools, they are insufficient to accurately determine the acceptance of a technology in its intended context of use, which is highly dependent on the diverse and dynamic requirements of its users, as we show here. As such, usability in the lab is unlikely to represent usability in the field. To demonstrate this, we first describe the results of a think-aloud usability study of our EUD tool “Jeeves”, followed by two case studies where Jeeves was used by psychologists in their work practices. Common issues in the artificial setting were seldom encountered in the real context of use, which instead unearthed new usability issues through unanticipated user needs. We conclude with considerations for usability evaluation of EUD tools that enable development of software for other users, including planning for collaborative activities, supporting developers to evaluate their own tools, and incorporating longitudinal methods of evaluation.Postprin
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