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

Absence of localization in a disordered one-dimensional ring threaded by an Aharonov-Bohm flux

Absence of localization is demonstrated analytically to leading order in weak disorder in a one-dimensional Anderson model of a ring threaded by an Aharonov-Bohm (A-B) flux. The result follows from adapting an earlier perturbation treatment of disorder in a superconducting ring subjected to an imaginary vector potential proportional to a depinning field for flux lines bound to random columnar defects parallel to the axis of the ring. The absence of localization in the ring threaded by an A-B flux for sufficiently weak disorder is compatible with large free electron type persistent current obtained in recent studies of the above model

Analytic Study of Persistent Current in a Two-Channel Disordered Mesoscopic Ring

We present an extensive analytical study of persistent current in a weakly disordered two-chain cylindrical ring threaded by an Aharonov-Bohm flux $0 < \phi <\phi_0/2$ (with $\phi_0$ the flux quantum) and described by the Anderson model. The effect of the disorder reveals a strong reduction of the persistent current for flux values near $\phi_0/4$. In conjunction with the pure system (zeroth order) current profile averaged over numbers of electrons and earlier results for the effect of disorder in one-dimensional rings, our two-channel results provide a simple interpretation of salient features of numerical results of Bouchiat and Montambaux (BM) for persistent current in an assembly of many-channel disordered rings. Single-channel (one-dimensional) effects are responsible for the dip in the persistent obtained by BM near $\phi=0$ and the corresponding peak near $\phi_0/2$, while the effect of disorder in independent channel pairs accounts for abrupt decreases of current superimposed to a continuous linear decay as the flux value $\phi_0/4$ is approached from above and from below, respectively. The persistent current in the two-channel ring involves a free particle current averaged over electron numbers of periodicity $\phi_0/2$, and a dominant disorder effect which has periodicity $\phi_0$.Comment: Accepted for publication in Phys. Rev.

Transmission, reflection and localization in a random medium with absorption or gain

We study reflection and transmission of waves in a random tight-binding system with absorption or gain for weak disorder, using a scattering matrix formalism. Our aim is to discuss analytically the effects of absorption or gain on the statistics of wave transport. Treating the effects of absorption or gain exactly in the limit of no disorder, allows us to identify short- and long lengths regimes relative to absorption- or gain lengths, where the effects of absorption/gain on statistical properties are essentially different. In the long-lengths regime we find that a weak absorption or a weak gain induce identical statistical corrections in the inverse localization length, but lead to different corrections in the mean reflection coefficient. In contrast, a strong absorption or a strong gain strongly suppress the effect of disorder in identical ways (to leading order), both in the localization length and in the mean reflection coefficient.Comment: Important revisions and expansion caused by a crucial property of $\hat Q

Enhancement of Persistent Current in Metal Rings by Correlated Disorder

We study analytically the effect of a correlated random potential on the persistent current in a one-dimensional ring threaded by a magnetic flux $\phi$, using an Anderson tight-binding model. In our model, the system of $N=2M$ atomic sites of the ring is assumed to be partitioned into $M$ pairs of identical nearest-neighbour sites (dimers). The site energies for different dimers are taken to be uncorrelated gaussian variables. For this system we obtain the exact flux-dependent energy levels to second order in the random site energies, using an earlier exact transfer matrix perturbation theory. These results are used to study the mean persistent current generated by $N_e\leq N$ spinless electrons occupying the $N_e$ lowest levels of the flux-dependent energy band at zero temperature. Detailed analyses are carried out in the limit $1\ll N_e\ll N$ and for a half-filled band ($N_e=N/2$), for magnetic fluxes $-1/2 <\phi/\phi_0<1/2$. While the uncorrelated disorder leads to a reduction of the persistent current, the disorder correlation acts to enhance it. In particular, in the half-filled band case the correlated disorder leads to a global flux-dependent enhancement of persistent current which has the same form for even and odd $N_e$. At low filling of the energy band the effect of the disorder on the persistent current is found to depend on the parity of $N_e$: the correlated disorder yields a reduction of the current for odd $N_e$ and an enhancement of the current for even $N_e$.Comment: 1

Mean Free Path in Disordered Multichannel Tight-Binding Wires

Transport in a disordered tight-binding wire involves a collection of different mean free paths resulting from the distinct fermi points, which correspond to the various scattering channels of the wire. The generalization of Thouless' relation between the mean free path and the localization length $\xi$ permits to define an average channel mean free path,$\bar\ell$, such that $\xi\sim N\bar\ell$ in an $N$-channel system. The averaged mean free path $\bar\ell$ is expressed exactly in terms of the total reflection coefficient of the wire and compared with the mean free path defined in the maximum entropy approach

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

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

Gender differences and inflammation: an in vitro model of blood cells stimulation in prepubescent children

Gender influences clinical presentations and markers in inflammatory diseases. In many chronic conditions, frequency of complications is greater in females, suggesting that continuous inflammatory reaction may induce greater damage in targeted organs and functions.Journal ArticleSCOPUS: ar.jinfo:eu-repo/semantics/publishe