Modeling Disordered Quantum Systems with Dynamical Networks

It is the purpose of the present article to show that so-called network models, originally designed to describe static properties of disordered electronic systems, can be easily generalized to quantum-{\em dynamical} models, which then allow for an investigation of dynamical and spectral aspects. This concept is exemplified by the Chalker-Coddington model for the Quantum Hall effect and a three-dimensional generalization of it. We simulate phase coherent diffusion of wave packets and consider spatial and spectral correlations of network eigenstates as well as the distribution of (quasi-)energy levels. Apart from that it is demonstrated how network models can be used to determine two-point conductances. Our numerical calculations for the three-dimensional model at the Metal-Insulator transition point delivers among others an anomalous diffusion exponent of $\eta = 3 - D_2 = 1.7 \pm 0.1$. The methods presented here in detail have been used partially in earlier work.Comment: 16 pages, Rev-TeX. to appear in Int. J. Mod. Phys.

Model of Electrostatic Actuated Deformable Mirror Using Strongly Coupled Electro-Mechanical Finite Element

The aim of this paper is to deal with multi-physics simulation of micro-electro-mechanical systems (MEMS) based on an advanced numerical methodology. MEMS are very small devices in which electric as well as mechanical and fluid phenomena appear and interact. Because of their microscopic scale, strong coupling effects arise between the different physical fields, and some forces, which were negligible at macroscopic scale, have to be taken into account. In order to accurately design such micro-electro-mechanical systems, it is of primary importance to be able to handle the strong coupling between the electric and the mechanical fields. In this paper, the finite element method (FEM) is used to model the strong coupled electro-mechanical interactions and to perform static and transient analyses taking into account large mesh displacements. These analyses will be used to study the behaviour of electrostatically actuated micro-mirrors.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

Visual sense of number vs. sense of magnitude in humans and machines

Numerosity perception is thought to be foundational to mathematical learning, but its computational bases are strongly debated. Some investigators argue that humans are endowed with a specialized system supporting numerical representations; others argue that visual numerosity is estimated using continuous magnitudes, such as density or area, which usually co-vary with number. Here we reconcile these contrasting perspectives by testing deep neural networks on the same numerosity comparison task that was administered to human participants, using a stimulus space that allows the precise measurement of the contribution of non-numerical features. Our model accurately simulates the psychophysics of numerosity perception and the associated developmental changes: discrimination is driven by numerosity, but non-numerical features also have a significant impact, especially early during development. Representational similarity analysis further highlights that both numerosity and continuous magnitudes are spontaneously encoded in deep networks even when no task has to be carried out, suggesting that numerosity is a major, salient property of our visual environment

Decoherence of encoded quantum registers

In order to eliminate disturbing effects of decoherence, encoding of quantum information in decoherence-free subspaces has been suggested. We analyze the benefits of this concept for a quantum register that is realized in a spin chain in contact with a common bosonic bath. Within a dissipation-less model we provide explicit analytical results for the average fidelity of plain and encoded quantum registers. For the investigation of dissipative spin-boson couplings we employ a master equation of Bloch-Redfield type.Comment: 13 pages, 9 figure

Approximate quantum error correction, random codes, and quantum channel capacity

We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This result is then used to analyze the average error correcting performance of codes that are randomly drawn from unitarily invariant code ensembles. Our results confirm that random codes of sufficiently large block size are highly suitable for quantum error correction. Moreover, employing a lemma of Bennett, Shor, Smolin, and Thapliyal, we prove that random coding attains information rates of the regularized coherent information.Comment: 29 pages, final version to appear in Phys. Rev. A, improved lower bound for code entanglement fidelity, simplified proo

Quantum Error Correction in Spatially Correlated Quantum Noise

We consider quantum error correction of quantum-noise that is created by a local interaction of qubits with a common bosonic bath. The possible exchange of bath bosons between qubits gives rise to spatial and temporal correlations in the noise. We find that these kind of noise correlations have a strong negative impact on quantum error correction.Comment: 4 pages, 1 figure, final version with minor correction

Coulomb drag between quantum wires with different electron densities

We study the way back-scattering electron--electron interaction generates Coulomb drag between quantum wires with different densities. At low temperature $T$ the system can undergo a commensurate-- incommensurate transition as the potential difference $|W|$ between the two wires passes a critical value $\Delta$, and this transition is reflected in a marked change in the dependence of drag resistivity on $W$ and $T$. At high temperature a density difference between the wires suppresses Coulomb drag induced by back scattering, and we use the Tomonaga--Luttinger model to study this suppression in detail.Comment: 6 pages, 4 figure

Point-Contact Conductances from Density Correlations

We formulate and prove an exact relation which expresses the moments of the two-point conductance for an open disordered electron system in terms of certain density correlators of the corresponding closed system. As an application of the relation, we demonstrate that the typical two-point conductance for the Chalker-Coddington model at criticality transforms like a two-point function in conformal field theory.Comment: 4 pages, 2 figure

Genetic diversity and population structure of the endangered Tanzanian Mpwapwa cattle breed

Mpwapwa cattle is a synthetic dual-purpose breed developed at the Mpwapwa Cattle Research Station, Tanzania, in the 1920s. The development and maintenance of Mpwapwa cattle have faced many challenges, and this breed has never been characterized at the genomic level. Our objectives were to assess the current genetic diversity and population structure of Mpwapwa cattle owing to its highly admixed origin and decline in active genetic management in recent years. Hair samples were collected from 251 cattle from different agro-ecological zones in Tanzania and were genotyped with the Bovine 100K SNP chip (Neogen Geneseek®). After quality control (using PLINK 1.9), we assessed heterozygosity (PLINK 1.9), inbreeding (detectRUNS package in R), and admixture (LEA package in R). We found the observed heterozygosity (0.32) was higher than the expected based on observed allele frequencies (0.29). Furthermore, more than 75% of studied animals had a runs-of-homozygosity-based inbreeding higher than 20%. Admixture analyses have indicated separation of the sampled animals by agro-ecological zones. Our results provide information for developing conservation and improvement strategies for this endangered Tanzania cattle breed

Electron scattering in multi-wall carbon-nanotubes

We analyze two scattering mechanisms that might cause intrinsic electronic resistivity in multi-wall carbon nanotubes: scattering by dopant impurities, and scattering by inter-tube electron-electron interaction. We find that for typically doped multi-wall tubes backward scattering at dopants is by far the dominating effect.Comment: 6 pages, 2 figures, to appear in Phys. Rev.