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

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 $P(s)$. 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 $P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly different from both the Brody distribution and from Izrailev's formula, and the best description is of the form $P(s)=c_1\,s\exp(-c_2\,s^{1+\beta})$, with $\beta\approx 0.2$. 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