A study of the entanglement in systems with periodic boundary conditions

We define the local periodic linking number, LK, between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions. The properties of LK indicate that it is an appropriate measure of entanglement between a collection of chains in a periodic system. Using this measure of linking to assess the extent of entanglement in a polymer melt we study the effect of CReTA algorithm on the entanglement of polyethylene chains. Our numerical results show that the statistics of the local periodic linking number observed for polymer melts before and after the application of CReTA are the same.Comment: 11 pages, 11 figure

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

Delocalization and conductance quantization in one-dimensional systems

We investigate the delocalization and conductance quantization in finite one-dimensional chains with only off-diagonal disorder coupled to leads. It is shown that the appearence of delocalized states at the middle of the band under correlated disorder is strongly dependent upon the even-odd parity of the number of sites in the system. In samples with inversion symmetry the conductance equals $2e^{2}/h$ for odd samples, and is smaller for even parity. This result suggests that this even-odd behaviour found previously in the presence of electron correlations may be unrelated to charging effects in the sample.Comment: submitted to PR

Mesoscopic simulations of crosslinked polymer networks

Institut für Theoretische Physik, Georg-August Universität, Göttingen, Germany E-mail: [email protected] Abstract. A new methodology and the corresponding C++ code for mesoscopic simulations of elastomers are presented. The test system, crosslinked cis-1,4-polyisoprene, is simulated with a Brownian Dynamics/kinetic Monte Carlo algorithm as a dense liquid of soft, coarse-grained beads, each representing 5-10 Kuhn segments. From the thermodynamic point of view, the system is described by a Helmholtz free-energy containing contributions from entropic springs between successive beads along a chain, slip-springs representing entanglements between beads on different chains, and non-bonded interactions. The methodology is employed for the calculation of the stress relaxation function from simulations of several microseconds at equilibrium, as well as for the prediction of stress-strain curves of crosslinked polymer networks under deformation. Introduction Atomistic and mesoscopic simulations are widely employed for the study of polymer systems, since they provide insights that are complementary to the information derived from experiments. Although the full-atom or united-atom representations provide an accurate description of polymers, their long relaxation time constitutes a severe obstacle to such approaches, and thus the development of mesoscopic (or coarse-grained) models is needed to cover longer time and length scales. One of the main characteristics of polymer melts and polymer networks is the entanglement effect, arising due to the uncrossability of polymer chains, which gives rise to complicated topological constraints [1]-[4]. The tube model, which considers a single chain in a mean field, is one of the most significant models for the description of entangled polymer

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

Griffiths-McCoy singularities in random quantum spin chains: Exact results through renormalization

The Ma-Dasgupta-Hu renormalization group (RG) scheme is used to study singular quantities in the Griffiths phase of random quantum spin chains. For the random transverse-field Ising spin chain we have extended Fisher's analytical solution to the off-critical region and calculated the dynamical exponent exactly. Concerning other random chains we argue by scaling considerations that the RG method generally becomes asymptotically exact for large times, both at the critical point and in the whole Griffiths phase. This statement is checked via numerical calculations on the random Heisenberg and quantum Potts models by the density matrix renormalization group method.Comment: 4 pages RevTeX, 2 figures include

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.