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

Stabilization of collapse and revival dynamics by a non-Markovian phonon bath

Semiconductor quantum dots (QDs) have been demonstrated to be versatile candidates to study the fundamentals of light-matter interaction [1-3]. In contrast with atom optics, dissipative processes are induced by the inherent coupling to the environment and are typically perceived as a major obstacle towards stable performances in experiments and applications [4]. In this paper we show that this is not necessarily the case. In fact, the memory of the environment can enhance coherent quantum optical effects. In particular, we demonstrate that the non-Markovian coupling to an incoherent phonon bath has a stabilizing effect on the coherent QD cavity-quantum electrodynamics (cQED) by inhibiting irregular oscillations and boosting regular collapse and revival patterns. For low photon numbers we predict QD dynamics that deviate dramatically from the well-known atomic Jaynes-Cummings model. Our proposal opens the way to a systematic and deliberate design of photon quantum effects via specifically engineered solid-state environments.Comment: 5 pages, 4 figure

Expression des "activated leukocyte cell adhesion molecule" im Mammakarzinom: Prädiktivität für das Ansprechen auf eine taxanfreie Chemotherapie

Zusammenfassung: Ziele: "Activated leukocyte cell adhesion molecule" (ALCAM) ist ein Oberflächenimmunglobulin und wird in vielen Mammakarzinomen exprimiert. Es wird vermutet, dass ALCAM in der Tumorgenese und -progression eine Rolle spielt. Die Bedeutung des Adhäsionsmoleküls ALCAM für das Ansprechen auf eine taxanfreie adjuvante Chemotherapie wurde untersucht. Material und Methoden: Gewebeproben von 162Patientinnen mit Mammakarzinomen wurden im Hinblick auf die Expression des ALCAM-Proteins untersucht. Immunhistologische Untersuchungen (IHC) und Western-Blot-Analysen (WB) wurden mit einem monoklonalen Antikörper gegen ALCAM durchgeführt. Die Proteinmengen im WB wurden densitometrisch quantifiziert und mit klinischen sowie histologischen Parametern korreliert. Die Ergebnisse wurden auf mRNA-Ebene mithilfe der Microarray-Analysen (Affymetrix) validiert. Ergebnisse: In der normalen Brustdrüse wird ALCAM in den luminalen und den basalen Epithelzellen exprimiert. Die WB-Analysen von Mammakarzinomen zeigen eine positive Korrelation der ALCAM-Expression mit dem Östrogenrezeptorstatus (p=0,04). Bei Patientinnen, die eine taxanfreie Chemotherapie erhalten haben, ist eine hohe ALCAM-Expression (WB, Affymetrix) prädikitiv für das Ansprechen einer Chemotherapie. Der mediane mRNA-Level von ALCAM war bei Patientinnen, die während des Beobachtungszeitraums noch lebten, 4,5-fach höher als bei Patientinnen, die verstarben. Schlussfolgerung: Ein hoher ALCAM-Gehalt korreliert positiv mit dem Östrogenrezeptorstatus. Außerdem ist ALCAM ein prädiktiver Faktor für das Ansprechen einer taxanfreien Chemotherapi

Diâmetro médio ponderado de partículas para estimativa de propriedades físico-hídricas dos solos.

O principal objetivo deste trabalho foi estimar características físico-hídricas do solo de difícil obtenção, através de modelos matemáticos baseados em variáveis das análises de rotina. Foram selecionados, em áreas de plantações florestais, 13 solos variando de 40 a 590 g kg-1 de conteúdo de argila. Nestes solos, foram obtidas amostras deformadas e indeformadas na camada de 5 cm a 15 cm, e realizadas, em laboratório, análises químicas (complexo sortivo, pH, acidez potencial) e físicas (densidade do solo, curva de retenção de umidade e porosidades). Estabeleceram-se correlações entre as variáveis umidade ótima do solo para compactação e umidade na capacidade de campo com todos os parâmetros químicos e físicos analisados. A característica do solo que apresentou o maior índice de correlação com umidade ótima (r = 0,95) e com capacidade de campo (r = 0,93) foi o diâmetro médio ponderado de partículas (DMPP). O DMPP pode ser obtido em todos os levantamentos de solo já realizados e é a soma da multiplicação entre o diâmetro médio das quatro frações granulométricas e suas concentrações no solo. A umidade do solo à -1500 kPa também se correlacionou com o DMPP (r = 0,93), o que permite estimar a quantidade de água disponível para as plantas

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 $g(r)$ decaying asymptotically as $r^{-\alpha}$. We study the dependence of the localization-length exponent $\nu$ on the correlation-strength exponent $\alpha$. % For fixed disorder $W$, there is a critical $\alpha_{\rm c}$, such that for $\alpha < \alpha_{\rm c}$, $\nu=2/\alpha$ and for $\alpha > \alpha_{\rm c}$, $\nu$ remains that of the uncorrelated system in accordance with the extended Harris criterion. At the band center, $\nu$ is independent of $\alpha$ but equal to that of the uncorrelated system. The physical mechanisms leading to this different behavior are discussed.Comment: submitted to Phys. Rev. Let

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

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

Behavior of the thermopower in amorphous materials at the metal-insulator transition

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