Quantum Hall effects in layered disordered superconductors

Layered singlet paired superconductors with disorder and broken time reversal symmetry are studied. The phase diagram demonstrates charge-spin separation in transport. In terms of the average intergrain transmission and the interlayer tunnelling we find quantum Hall phases with spin Hall coefficients of 0 and 2 separated by a spin metal phase. We identify a spin metal-insulator localization exponent as well as a spin conductivity exponent of ~0.9. In presence of a Zeeman term an additional phase with spin Hall coefficient of 1 appears.Comment: 4 pages, 4 figure

Level statistics for quantum Hall systems

Level statistics for two classes of disordered systems at criticality are analyzed in terms of different realizations of the Chalker–Coddington network model. These include: 1) Re-examination of the standard U(1) model describing dynamics of electrons on the lowest Landau level in the quantum Hall effect, where it is shown that after proper local unfolding the nearest-neighbor spacing distribution (NNSD) at the critical energy follows the Wigner surmise for Gaussian unitary ensembles (GUE). 2) Quasi-particles in disordered superconductors with broken time reversal and spin rotation invariance (in the language of random matrix theory this system is a representative of symmetry class D in the classification scheme of Altland and Zirnbauer). Here again the NNSD obeys the Wigner surmise for GUE, reflecting therefore only «basic» discrete symmetries of the system (time reversal violation) and ignoring particle–hole symmetries and other finer details (criticality). In the localized regime level repulsion is suppressed

Non-linear supersymmetric Sigma-Model for Diffusive Scattering of Classical Waves with Resonance Enhancement

We derive a non-linear sigma-model for the transport of light (classical waves) through a disordered medium. We compare this extension of the model with the well-established non-linear sigma-model for the transport of electrons (Schroedinger waves) and display similarities of and differences between both cases. Motivated by experimental work (M. van Albada et al., Phys. Rev. Lett. 66 (1991) 3132), we then generalize the non-linear sigma-model further to include resonance scattering. We find that the form of the effective action is unchanged but that a parameter of the effective action, the mean level density, is modified in a manner which correctly accounts for the data.Comment: 4 pages, 1 Figure, to be published in Europhysics Letter

Plateaux Transitions in the Pairing Model:Topology and Selection Rule

Based on the two-dimensional lattice fermion model, we discuss transitions between different pairing states. Each phase is labeled by an integer which is a topological invariant and characterized by vortices of the Bloch wavefunction. The transitions between phases with different integers obey a selection rule. Basic properties of the edge states are revealed. They reflect the topological character of the bulk. Transitions driven by randomness are also discussed numerically.Comment: 8 pages with 2 postscript figures, RevTe

Thermal metal in network models of a disordered two-dimensional superconductor

We study the universality class for localization which arises from models of non-interacting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotation symmetries. Two-dimensional systems in this category, which is known as class D, can display phases with three different types of quasiparticle dynamics: metallic, localized, or with a quantized (thermal) Hall conductance. Correspondingly, they can show a variety of delocalization transitions. We illustrate this behavior by investigating numerically the phase diagrams of network models with the appropriate symmetry, and for the first time show the appearance of the metallic phase.Comment: 5 pages, 3 figure

Localization and conductance fluctuations in the integer quantum Hall effect: Real--space renormalization group approach

We consider the network model of the integer quantum Hall effect transition. By generalizing the real--space renormalization group procedure for the classical percolation to the case of quantum percolation, we derive a closed renormalization group (RG) equation for the universal distribution of conductance of the quantum Hall sample at the transition. We find an approximate solution of the RG equation and use it to calculate the critical exponent of the localization length and the central moments of the conductance distribution. The results obtained are compared with the results of recent numerical simulations.Comment: 17 pages, RevTex, 7 figure

Landau level mixing and spin degeneracy in the quantum Hall effect

We study dynamics of electrons in a magnetic field using a network model with two channels per link with random mixing in a random intrachannel potential; the channels represent either two Landau levels or two spin states. We consider channel mixing as function of the energy separation of the two extended states and show that its effect changes from repulsion to attraction as the energy separation increases. For two Landau levels this leads to level floating at low magnetic fields while for Zeeman split spin states we predict level attraction at high magnetic fields, accounting for ESR data. We also study random mixing of two degenerate channels, while the intrachannel potential is periodic (non-random). We find a single extended state with a localization exponent $\nu\approx 1.1$ for real scattering at nodes; the general case has also a single extended state, though the localized nature of nearby states sets in at unusually large scales.Comment: 18 pages, 11 tex-files and 1 ps-file of figure

Doublet method for very fast autocoding

BACKGROUND: Autocoding (or automatic concept indexing) occurs when a software program extracts terms contained within text and maps them to a standard list of concepts contained in a nomenclature. The purpose of autocoding is to provide a way of organizing large documents by the concepts represented in the text. Because textual data accumulates rapidly in biomedical institutions, the computational methods used to autocode text must be very fast. The purpose of this paper is to describe the doublet method, a new algorithm for very fast autocoding. METHODS: An autocoder was written that transforms plain-text into intercalated word doublets (e.g. "The ciliary body produces aqueous humor" becomes "The ciliary, ciliary body, body produces, produces aqueous, aqueous humor"). Each doublet is checked against an index of doublets extracted from a standard nomenclature. Matching doublets are assigned a numeric code specific for each doublet found in the nomenclature. Text doublets that do not match the index of doublets extracted from the nomenclature are not part of valid nomenclature terms. Runs of matching doublets from text are concatenated and matched against nomenclature terms (also represented as runs of doublets). RESULTS: The doublet autocoder was compared for speed and performance against a previously published phrase autocoder. Both autocoders are Perl scripts, and both autocoders used an identical text (a 170+ Megabyte collection of abstracts collected through a PubMed search) and the same nomenclature (neocl.xml, containing over 102,271 unique names of neoplasms). In side-by-side comparison on the same computer, the doublet method autocoder was 8.4 times faster than the phrase autocoder (211 seconds versus 1,776 seconds). The doublet method codes 0.8 Megabytes of text per second on a desktop computer with a 1.6 GHz processor. In addition, the doublet autocoder successfully matched terms that were missed by the phrase autocoder, while the phrase autocoder found no terms that were missed by the doublet autocoder. CONCLUSIONS: The doublet method of autocoding is a novel algorithm for rapid text autocoding. The method will work with any nomenclature and will parse any ascii plain-text. An implementation of the algorithm in Perl is provided with this article. The algorithm, the Perl implementation, the neoplasm nomenclature, and Perl itself, are all open source materials

Decoherence of a particle in a ring

We consider a particle coupled to a dissipative environment and derive a perturbative formula for the dephasing rate based on the purity of the reduced probability matrix. We apply this formula to the problem of a particle on a ring, that interacts with a dirty metal environment. At low but finite temperatures we find a dephasing rate $\propto T^{3/2}$, and identify dephasing lengths for large and for small rings. These findings shed light on recent Monte Carlo data regarding the effective mass of the particle. At zero temperature we find that spatial fluctuations suppress the possibility of having a power law decay of coherence.Comment: 5 pages, 1 figure, proofed version to be published in EP

Dephasing of a particle in a dissipative environment

The motion of a particle in a ring of length L is influenced by a dirty metal environment whose fluctuations are characterized by a short correlation distance $\ell << L$. We analyze the induced decoherence process, and compare the results with those obtained in the opposing Caldeira-Leggett limit ($\ell >> L$). A proper definition of the dephasing factor that does not depend on a vague semiclassical picture is employed. Some recent Monte-Carlo results about the effect of finite temperatures on "mass renormalization" in this system are illuminated.Comment: 18 pages, 2 figures, some textual improvements, to be published in JP