Enhanced quantum tunnelling induced by disorder

We reconsider the problem of the enhancement of tunnelling of a quantum particle induced by disorder of a one-dimensional tunnel barrier of length $L$, using two different approximate analytic solutions of the invariant imbedding equations of wave propagation for weak disorder. The two solutions are complementary for the detailed understanding of important aspects of numerical results on disorder-enhanced tunnelling obtained recently by Kim et al. (Phys. rev. B{\bf 77}, 024203 (2008)). In particular, we derive analytically the scaled wavenumber $(kL)$-threshold where disorder-enhanced tunnelling of an incident electron first occurs, as well as the rate of variation of the transmittance in the limit of vanishing disorder. Both quantities are in good agreement with the numerical results of Kim et al. Our non-perturbative solution of the invariant imbedding equations allows us to show that the disorder enhances both the mean conductance and the mean resistance of the barrier.Comment: 10 page

Flux Dependence of Persistent Current in a Mesoscopic Disordered Tight Binding Ring

We reconsider the study of persistent currents in a disordered one-dimensional ring threaded by a magnetic flux, using he one-band tight-binding model for a ring of N-sites with random site energies. The secular equation for the eigenenergies expressed in terms of transfer matrices in the site representation is solved exactly to second order in a perturbation theory for weak disorder and fluxes differing from half-integer multiples of the elementary flux quantum. From the equilibrium currents associated with the one-electron eigenstates we derive closed analytic expressions for the disorder averaged persistent current for even and odd numbers, Ne, of electrons in the ground state. Explicit discussion for the half-filled band case confirms that the persistent current is flux periodic as in the absence of disorder, and that its amplitude is generally suppressed by the effect of the disorder. In comparison to previous results, based on an approximate analysis of the secular equation, the current suppression by disorder is strongly enhanced by a new flux-dependent factor.Comment: 15 pages, LaTex 2

Conductance and localization in disordered wires: role of evanescent states

This paper extends an earlier analytical scattering matrix treatment of conductance and localization in coupled two- and three Anderson chain systems for weak disorder when evanescent states are present at the Fermi level. Such states exist typically when the interchain coupling exceeds the width of propagating energy bands associated with the various transverse eigenvalues of the coupled tight-binding systems. We calculate reflection- and transmission coefficients in cases where, besides propagating states, one or two evanescent states are available at the Fermi level for elastic scattering of electrons by the disordered systems. We observe important qualitative changes in these coefficients and in the related localization lengths due to ineffectiveness of the evanescent modes for transmission and reflection in the various scattering channels. In particular, the localization lengths are generally significantly larger than the values obtained when evanescent modes are absent. Effects associated with disorder mediated coupling between propagating and evanescent modes are shown to be suppressed by quantum interference effects, in lowest order for weak disorder

Enhanced Transmission Through Disordered Potential Barrier

Effect of weak disorder on tunneling through a potential barrier is studied analytically. A diagrammatic approach based on the specific behavior of subbarrier wave functions is developed. The problem is shown to be equivalent to that of tunneling through rectangular barriers with Gaussian distributed heights. The distribution function for the transmission coefficient $T$ is derived, and statistical moments \left are calculated. The surprising result is that in average disorder increases both tunneling conductance and resistance.Comment: 10 pages, REVTeX 3.0, 2 figures available upon reques

Exact transmission moments in one-dimensional weak localization and single-parameter scaling

We obtain for the first time the expressions for the mean and the variance of the transmission coefficient for an Anderson chain in the weak localization regime, using exact expansions of the complex transmission- and reflection coefficients to fourth order in the weakly disordered site energies. These results confirm the validity of single-parameter scaling theory in a domain where the higher transmission cumulants may be neglected. We compare our results with earlier results for transmission cumulants in the weak localization domain based on the phase randomization hypothesis

Theory of Second and Higher Order Stochastic Processes

This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial example is $\ddot x = R(t)$, where $R(t)$ is not a Gaussian white noise). The stochastic process is discretized into $n$ time-steps, all possible realizations are summed up and the continuum limit is taken. This procedure often yields closed form formulas for the joint probability distributions. Completely worked out examples include all Gaussian random forces and a large class of Markovian (non-Gaussian) forces. This approach is also useful for deriving Fokker-Planck equations for the probability distribution functions. This is worked out for Gaussian noises and for the Markovian dichotomous noise.Comment: 35 pages, PlainTex, accepted for publication in Phys Rev. E

Localization-delocalization transition in the quasi-one-dimensional ladder chain with correlated disorder

The generalization of the dimer model on a two-leg ladder is defined and investigated both, analytically and numerically. For the closed system we calculate the Landauer resistance analytically and found the presence of the point of delocalization at the band center which is confirmed by the numerical calculations of the Lyapunov exponent. We calculate also analytically the localization length index and present the numerical investigations of the density of states (DOS). For the open counterpart of this model the distribution of the Wigner delay times is calculated numerically. It is shown how the localization-delocalization transition manifest itself in the behavior of the distribution.Comment: 9 pages, 10 figures, Revte

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

Localization fom conductance in few-channel disordered wires

We study localization in two- and three channel quasi-1D systems using multichain tight-binding Anderson models with nearest-neighbour interchain hopping. In the three chain case we discuss both the case of free- and that of periodic boundary conditions between the chains. The finite disordered wires are connected to ideal leads and the localization length is defined from the Landauer conductance in terms of the transmission coefficients matrix. The transmission- and reflection amplitudes in properly defined quantum channels are obtained from S-matrices constructed from transfer matrices in Bloch wave bases for the various quasi-1D systems. Our exact analytic expressions for localization lengths for weak disorder reduce to the Thouless expression for 1D systems in the limit of vanishing interchain hopping. For weak interchain hopping the localization length decreases with respect to the 1D value in all three cases. In the three-channel cases it increases with interchain hopping over restricted domains of large hopping

Cell permeable stapled peptide inhibitor of Wnt signaling that targets β-catenin protein‒protein interactions

The Wnt signaling pathway plays a critical role in cell proliferation and differentiation, thus it is often associated with diseases such as cancers. Unfortunately, although attractive, developing anti-cancer strategy targeting Wnt signaling has been challenging given that the most attractive targets are involved in protein-protein interactions (PPIs). Here, we develop a stapled peptide inhibitor that targets the interaction between β-catenin and T cell factor/lymphoid enhancer-binding factor transcription factors, which are crucially involved in Wnt signaling. Our integrative approach combines peptide stapling to optimize proteolytic stability, with lessons learned from cell-penetrating peptide (CPP) design to maximize cellular uptake resulting in NLS-StAx-h, a selective, cell permeable, stapled peptide inhibitor of oncogenic Wnt signaling that efficiently inhibits β-catenin-transcription factor interactions. We expect that this type of integrative strategy that endows stapled peptides with CPP features will be generally useful for developing inhibitors of intracellular PPIs