Localization length in Dorokhov's microscopic model of multichannel wires

We derive exact quantum expressions for the localization length $L_c$ for weak disorder in two- and three chain tight-binding systems coupled by random nearest-neighbour interchain hopping terms and including random energies of the atomic sites. These quasi-1D systems are the two- and three channel versions of Dorokhov's model of localization in a wire of $N$ periodically arranged atomic chains. We find that $L^{-1}_c=N.\xi^{-1}$ for the considered systems with $N=(1,2,3)$, where $\xi$ is Thouless' quantum expression for the inverse localization length in a single 1D Anderson chain, for weak disorder. The inverse localization length is defined from the exponential decay of the two-probe Landauer conductance, which is determined from an earlier transfer matrix solution of the Schr\"{o}dinger equation in a Bloch basis. Our exact expressions above differ qualitatively from Dorokhov's localization length identified as the length scaling parameter in his scaling description of the distribution of the participation ratio. For N=3 we also discuss the case where the coupled chains are arranged on a strip rather than periodically on a tube. From the transfer matrix treatment we also obtain reflection coefficients matrices which allow us to find mean free paths and to discuss their relation to localization lengths in the two- and three channel systems

Numerical renormalization-group study of spin correlations in one-dimensional random spin chains

We calculate the ground-state two-spin correlation functions of spin-1/2 quantum Heisenberg chains with random exchange couplings using the real-space renormalization group scheme. We extend the conventional scheme to take account of the contribution of local higher multiplet excitations in each decimation step. This extended scheme can provide highly accurate numerical data for large systems. The random average of staggered spin correlations of the chains with random antiferromagnetic (AF) couplings shows algebraic decay like $1/r^2$, which verifies the Fisher's analytic results. For chains with random ferromagnetic (FM) and AF couplings, the random average of generalized staggered correlations is found to decay more slowly than a power-law, in the form close to $1/\ln(r)$. The difference between the distribution functions of the spin correlations of the random AF chains and of the random FM-AF chains is also discussed.Comment: 14 pages including 8 figures, REVTeX, submitted to Physical Review

Retrotransposon activation contributes to neurodegeneration in a Drosophila TDP-43 model of ALS

Amyotrophic lateral sclerosis (ALS) and frontotemporal lobar degeneration (FTLD) are two incurable neurodegenerative disorders that exist on a symptomological spectrum and share both genetic underpinnings and pathophysiological hallmarks. Functional abnormality of TAR DNA-binding protein 43 (TDP-43), an aggregation-prone RNA and DNA binding protein, is observed in the vast majority of both familial and sporadic ALS cases and in ~40% of FTLD cases, but the cascade of events leading to cell death are not understood. We have expressed human TDP-43 (hTDP-43) in Drosophila neurons and glia, a model that recapitulates many of the characteristics of TDP-43-linked human disease including protein aggregation pathology, locomotor impairment, and premature death. We report that such expression of hTDP-43 impairs small interfering RNA (siRNA) silencing, which is the major post-transcriptional mechanism of retrotransposable element (RTE) control in somatic tissue. This is accompanied by de-repression of a panel of both LINE and LTR families of RTEs, with somewhat different elements being active in response to hTDP-43 expression in glia versus neurons. hTDP-43 expression in glia causes an early and severe loss of control of a specific RTE, the endogenous retrovirus (ERV) gypsy. We demonstrate that gypsy causes the degenerative phenotypes in these flies because we are able to rescue the toxicity of glial hTDP-43 either by genetically blocking expression of this RTE or by pharmacologically inhibiting RTE reverse transcriptase activity. Moreover, we provide evidence that activation of DNA damage-mediated programmed cell death underlies both neuronal and glial hTDP-43 toxicity, consistent with RTE-mediated effects in both cell types. Our findings suggest a novel mechanism in which RTE activity contributes to neurodegeneration in TDP-43-mediated diseases such as ALS and FTLD

Conductance scaling at the band center of wide wires with pure non--diagonal disorder

Kubo formula is used to get the scaling behavior of the static conductance distribution of wide wires showing pure non-diagonal disorder. Following recent works that point to unusual phenomena in some circumstances, scaling at the band center of wires of odd widths has been numerically investigated. While the conductance mean shows a decrease that is only proportional to the inverse square root of the wire length, the median of the distribution exponentially decreases as a function of the square root of the length. Actually, the whole distribution decays as the inverse square root of the length except close to G=0 where the distribution accumulates the weight lost at larger conductances. It accurately follows the theoretical prediction once the free parameter is correctly fitted. Moreover, when the number of channels equals the wire length but contacts are kept finite, the conductance distribution is still described by the previous model. It is shown that the common origin of this behavior is a simple Gaussian statistics followed by the logarithm of the E=0 wavefunction weight ratio of a system showing chiral symmetry. A finite value of the two-dimensional conductance mean is obtained in the infinite size limit. Both conductance and the wavefunction statistics distributions are given in this limit. This results are consistent with the 'critical' character of the E=0 wavefunction predicted in the literature.Comment: 10 pages, 9 figures, RevTeX macr

Random-mass Dirac fermions in an imaginary vector potential: Delocalization transition and localization length

One dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix methods which we developed recently. We investigate the effects of nonlocal correlation of the spatial-varying Dirac mass on the delocalization transition. Especially we numerically calculate both the "typical" and "mean" localization lengths as a function of energy and the correlation length of the random mass. To this end we introduce an imaginary vector potential as suggested by Hatano and Nelson and solve the eigenvalue problem. Numerical calculations are in good agreement with the results of the analytical calculations.Comment: 4 page

Magnon delocalization in ferromagnetic chains with long-range correlated disorder

We study one-magnon excitations in a random ferromagnetic Heisenberg chain with long-range correlations in the coupling constant distribution. By employing an exact diagonalization procedure, we compute the localization length of all one-magnon states within the band of allowed energies $E$. The random distribution of coupling constants was assumed to have a power spectrum decaying as $S(k)\propto 1/k^{\alpha}$. We found that for $\alpha < 1$, one-magnon excitations remain exponentially localized with the localization length $\xi$ diverging as 1/E. For $\alpha = 1$ a faster divergence of $\xi$ is obtained. For any $\alpha > 1$, a phase of delocalized magnons emerges at the bottom of the band. We characterize the scaling behavior of the localization length on all regimes and relate it with the scaling properties of the long-range correlated exchange coupling distribution.Comment: 7 Pages, 5 figures, to appear in Phys. Rev.

Looking for life on Mars with the Rosalind Franklin rover: the PanCam instrument

The ESA-Russia Rosalind Franklin (ExoMars 2022) rover, with its unique 2m drill, will address key questions in the search for life on Mars. PanCam will establish the surface context, with other instruments, providing geology, atmospheric science and 3D vision. PanCam uses a pair of Wide Angle Cameras (WACs), each with an 11 position filter wheel, and a High Resolution Camera (HRC). The cameras and electronics are in an optical bench that provides the interface to the rover and planetary protection. PanCam includes a calibration target mounted on the rover deck for radiometric calibration, fiducial markers for geometric calibration and a rover inspection mirror

Effects of a nanoscopic filler on the structure and dynamics of a simulated polymer melt and the relationship to ultra-thin films

We perform molecular dynamics simulations of an idealized polymer melt surrounding a nanoscopic filler particle to probe the effects of a filler on the local melt structure and dynamics. We show that the glass transition temperature $T_g$ of the melt can be shifted to either higher or lower temperatures by appropriately tuning the interactions between polymer and filler. A gradual change of the polymer dynamics approaching the filler surface causes the change in the glass transition. We also find that while the bulk structure of the polymers changes little, the polymers close to the surface tend to be elongated and flattened, independent of the type of interaction we study. Consequently, the dynamics appear strongly influenced by the interactions, while the melt structure is only altered by the geometric constraints imposed by the presence of the filler. Our findings show a strong similarity to those obtained for ultra-thin polymer films (thickness $\lesssim 100$ nm) suggesting that both ultra-thin films and filled-polymer systems might be understood in the same context

Management of nystagmus in children : a review of the literature and current practice in UK specialist services

Nystagmus is an eye movement disorder characterised by abnormal, involuntary rhythmic oscillations of one or both eyes, initiated by a slow phase. It is not uncommon in the UK and regularly seen in paediatric ophthalmology and adult general/strabismus clinics. In some cases, it occurs in isolation, and in others, it occurs as part of a multisystem disorder, severe visual impairment or neurological disorder. Similarly, in some cases, visual acuity can be normal and in others can be severely degraded. Furthermore, the impact on vision goes well beyond static acuity alone, is rarely measured and may vary on a minute-to-minute, day-to-day or month-to-month basis. For these reasons, management of children with nystagmus in the UK is varied, and patients report hugely different experiences and investigations. In this review, we hope to shine a light on the current management of children with nystagmus across five specialist centres in the UK in order to present, for the first time, a consensus on investigation and clinical management