Conductance of 1D quantum wires with anomalous electron-wavefunction localization

We study the statistics of the conductance $g$ through one-dimensional disordered systems where electron wavefunctions decay spatially as $|\psi| \sim \exp (-\lambda r^{\alpha})$ for $0 <\alpha <1$, $\lambda$ being a constant. In contrast to the conventional Anderson localization where $|\psi| \sim \exp (-\lambda r)$ and the conductance statistics is determined by a single parameter: the mean free path, here we show that when the wave function is anomalously localized ($\alpha <1$) the full statistics of the conductance is determined by the average $$ and the power $\alpha$. Our theoretical predictions are verified numerically by using a random hopping tight-binding model at zero energy, where due to the presence of chiral symmetry in the lattice there exists anomalous localization; this case corresponds to the particular value $\alpha =1/2$. To test our theory for other values of $\alpha$, we introduce a statistical model for the random hopping in the tight binding Hamiltonian.Comment: 6 pages, 8 figures. Few changes in the presentation and references updated. Published in PRB, Phys. Rev. B 85, 235450 (2012

Meniere's disease

Meniere's disease is one of the most common causes of recurrent vestibular vertigo. Despite its comparatively high prevalence, this disease is frequently diagnosed late and patients do not receive timely therapy. The paper gives current diagnostic criteria for Meniere's disease. Approaches to treating the disease in its attack and an interattack interval are discussed. Emphasis is laid on the role of vestibular rehabilitation in increasing the quality of life in patients with Meniere's disease

The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field

Let k be a global field and let k_v be the completion of k with respect to v, a non-archimedean place of k. Let \mathbf{G} be a connected, simply-connected algebraic group over k, which is absolutely almost simple of k_v-rank 1. Let G=\mathbf{G}(k_v). Let \Gamma be an arithmetic lattice in G and let C=C(\Gamma) be its congruence kernel. Lubotzky has shown that C is infinite, confirming an earlier conjecture of Serre. Here we provide complete solution of the congruence subgroup problem for \Gamm$ by determining the structure of C. It is shown that C is a free profinite product, one of whose factors is \hat{F}_{\omega}, the free profinite group on countably many generators. The most surprising conclusion from our results is that the structure of C depends only on the characteristic of k. The structure of C is already known for a number of special cases. Perhaps the most important of these is the (non-uniform) example \Gamma=SL_2(\mathcal{O}(S)), where \mathcal{O}(S) is the ring of S-integers in k, with S=\{v\}, which plays a central role in the theory of Drinfeld modules. The proof makes use of a decomposition theorem of Lubotzky, arising from the action of \Gamma on the Bruhat-Tits tree associated with G.Comment: 27 pages, 5 figures, to appear in J. Reine Angew. Mat

Statistics of the One-Electron Current in a One-Dimensional Mesoscopic Ring at Arbitrary Magnetic Fields

The set of moments and the distribution function of the one-electron current in a one-dimensional disordered ring with arbitrary magnetic flux are calculated.Comment: 10 pages; Plain TeX; IFUM 448/FT; to appear in J. Stat. Phy

Theory of the Eigler-swith

We suggest a simple model to describe the reversible field-induced transfer of a single Xe-atom in a scanning tunneling microscope, --- the Eigler-switch. The inelasticly tunneling electrons give rise to fluctuating forces on and damping of the Xe-atom resulting in an effective current dependent temperature. The rate of transfer is controlled by the well-known Arrhenius law with this effective temperature. The directionality of atom transfer is discussed, and the importance of use of non-equlibrium-formalism for the electronic environment is emphasized. The theory constitutes a formal derivation and generalization of the so-called Desorption Induced by Multiple Electron Transitions (DIMET) point of view.Comment: 13 pages (including 2 figures in separate LaTeX-files with ps-\specials), REVTEX 3.

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

Exact Solution for the Distribution of Transmission Eigenvalues in a Disordered Wire and Comparison with Random-Matrix Theory

An exact solution is presented of the Fokker-Planck equation which governs the evolution of an ensemble of disordered metal wires of increasing length, in a magnetic field. By a mapping onto a free-fermion problem, the complete probability distribution function of the transmission eigenvalues is obtained. The logarithmic eigenvalue repulsion of random-matrix theory is shown to break down for transmission eigenvalues which are not close to unity. ***Submitted to Physical Review B.****Comment: 20 pages, REVTeX-3.0, INLO-PUB-931028

Vortex-core properties and vortex-lattice transformation in FeSe

Low-temperature scanning tunneling microscopy and spectroscopy has been used to image the vortex core and the vortex lattice in FeSe single crystals. The local tunneling spectra acquired at the center of elliptical vortex cores display a strong particle-hole asymmetry with spatial oscillation, characteristic of the quantum-limit vortex core. Furthermore, a quasihexagonal vortex lattice at low magnetic field undergoes noticeable rhombic distortions above a certain field ∼1.5 T. This field H∗ also reveals itself as a kink in the magnetic field dependence of the specific heat. The observation of a nearly hexagonal vortex lattice at low field is very surprising for materials with an orthorhombic crystal structure and it is in apparent contradiction with the elliptical shape of the vortex cores. These observations can be directly connected to the multiband nature of superconductivity in this material, provided we attribute them to the suppression of superconducting order parameter in one of the energy bands. Above the field H∗ the superconducting coherence length for this band can well exceed the intervortex distance which strengthens the nonlocal effects. Therefore, in addition to multiple-band effects, other possible sources that can contribute to the observed evolution of the vortex-lattice structure include nonlocal effects which cause the field-dependent interplay between the symmetry of the crystal and vortex lattice or the magnetoelastic interactions due to the strain field generated by vortices. © 2019 American Physical Society.Citrus Research and Development Foundation, CRDFGovernment Council on Grants, Russian FederationRussian Science Foundation, RSF: 17-12-01383, 18-72-10027Ministero dellâ Istruzione, dellâ Università e della Ricerca, MIURFoundation for the Advancement of Theoretical Physics and Mathematics: 17-11-109Ministero dellâ Istruzione, dellâ Università e della Ricerca, MIURKazan Federal UniversityOffice of Science, SCDivision of Materials Sciences and Engineering, DMSERussian Foundation for Basic Research, RFBR: 17-52-12044Ministry of Education and Science of the Russian Federation, MinobrnaukaTemple University, TUArgonne National Laboratory, ANLNanjing University of Science and Technology, NUST: K2-2017-084Drexel UniversityThe authors would like to acknowledge fruitful discussions with V. Kogan and T. Hanaguri. We also would like to acknowledge technical support during the early stage of these measurements from S. A. Moore. The work at Temple University, where low temperature scanning tunneling measurements were performed, was supported by US Department of Energy, Office of Science, Basic Energy Science, Materials Sciences and Engineering Division under Award No. DE-SC0004556. The work at Drexel University and at the M.V. Lomonosov Moscow State University was supported by the US Civilian Research and Development Foundation (CRDF Global). The work in Russia has been supported in part by the Ministry of Education and Science of the Russian Federation in the framework of the Increase Competitiveness Program of NUST MISiS Grant K2-2017-084, by Act 211 of the Government of Russian Federation, Contracts No. 02.A03.21.0004, No. 02.A03.21.0006, and No. 02.A03.21.0011 and by the Russian Government Program of Competitive Growth of Kazan Federal University. One of the authors (C.D.G.) would like to acknowledge partial support from MIUR (Ministry of Education, Universities and Research of the Italian Government). The work in IPM RAS (Nizhny Novgorod) was supported in part by the Russian Science Foundation (the calculation of the vortex-lattice characteristics Grant No. 18-72-10027; the calculation of the vortex-core deformation and the analysis of the experimental data Grant No. 17-12-01383), the Russian Foundation for Basic Research (Grant No. 17-52-12044), and Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (Grant No. 17-11-109). The work at Argonne National Laboratory was supported by the US Department of Energy, Office of Science, Basic Energy Science, Materials Sciences and Engineering Division

Nonlogarithmic repulsion of transmission eigenvalues in a disordered wire

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