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

Characteristics of ferroelectric-ferroelastic domains in N{\'e}el-type skyrmion host GaV4_4S8_8

GaV$_4$S$_8$ is a multiferroic semiconductor hosting N{\'e}el-type magnetic skyrmions dressed with electric polarization. At T$_s$ = 42K, the compound undergoes a structural phase transition of weakly first-order, from a non-centrosymmetric cubic phase at high temperatures to a polar rhombohedral structure at low temperatures. Below T$_s$, ferroelectric domains are formed with the electric polarization pointing along any of the four $\left< 111 \right>$ axes. Although in this material the size and the shape of the ferroelectric-ferroelastic domains may act as important limiting factors in the formation of the N{\'e}el-type skyrmion lattice emerging below T$_C$=13\:K, the characteristics of polar domains in GaV$_4$S$_8$ have not been studied yet. Here, we report on the inspection of the local-scale ferroelectric domain distribution in rhombohedral GaV$_4$S$_8$ using low-temperature piezoresponse force microscopy. We observed mechanically and electrically compatible lamellar domain patterns, where the lamellae are aligned parallel to the (100)-type planes with a typical spacing between 100 nm-1.2 $\mu$m. We expect that the control of ferroelectric domain size in polar skyrmion hosts can be exploited for the spatial confinement and manupulation of N{\'e}el-type skyrmions

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 $W_c$ are consistent with results of previous studies, including the transfer-matrix method and multifractal analysis of the wave functions. $W_c$ 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 $\nu=1.45\pm0.2$. 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