Exact Random Walk Distributions using Noncommutative Geometry

Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $N$ on a two-dimensional square lattice for large $N$, taking into account finite size contributions.Comment: Latex, 3 pages, 1 figure, to be published in J. Phys. A : Math. Ge

Method of studying the Bogoliubov-de Gennes equations for the superconducting vortex lattice state

In this paper, we present a method to construct the eigenspace of the normal-state electrons moving in a 2D square lattice in presence of a perpendicular uniform magnetic field which imposes (quasi)-periodic boundary conditions for the wave functions in the magnetic unit cell. An exact unitary transformations are put forward to correlate the discrete eigenvectors of the 2D electrons with those of the Harper's equation. The cyclic-tridiagonal matrix associated with the Harper's equation is then tridiagonalized by another unitary transformation. The obtained eigenbasis is utilized to expand the Bogoliubov-de Gennes equations for the superconducting vortex lattice state, which showing the merit of our method in studying the large-sized system. To test our method, we have applied our results to study the vortex lattice state of an s-wave superconductor.Comment: 8 pages; 3 figure

Dependent Types for Pragmatics

This paper proposes the use of dependent types for pragmatic phenomena such as pronoun binding and presupposition resolution as a type-theoretic alternative to formalisms such as Discourse Representation Theory and Dynamic Semantics.Comment: This version updates the paper for publication in LEU

Exponential localization in one-dimensional quasiperiodic optical lattices

We investigate the localization properties of a one-dimensional bichromatic optical lattice in the tight binding regime, by discussing how exponentially localized states emerge upon changing the degree of commensurability. We also review the mapping onto the discrete Aubry-Andre' model, and provide evidences on how the momentum distribution gets modified in the crossover from extended to exponentially localized states. This analysis is relevant to the recent experiment on Anderson localization of a noninteracting Bose-Einstein condensate in a quasiperiodic optical lattice [G. Roati et al., Nature 453, 895 (2008)].Comment: 13 pages, 6 figure

Magnetic Field Effect on the Pseudogap Temperature within Precursor Superconductivity

We determine the magnetic field dependence of the pseudogap closing temperature T* within a precursor superconductivity scenario. Detailed calculations with an anisotropic attractive Hubbard model account for a recently determined experimental relation in BSCCO between the pseudogap closing field and the pseudogap temperature at zero field, as well as for the weak initial dependence of T* at low fields. Our results indicate that the available experimental data are fully compatible with a superconducting origin of the pseudogap in cuprate superconductors.Comment: 4 pages, 3 figure

Effects of Electron Correlations on Hofstadter Spectrum

By allowing interactions between electrons, a new Harper's equation is derived to examine the effects of electron correlations on the Hofstadter energy spectra. It is shown that the structure of the Hofstadter butterfly ofr the system of correlated electrons is modified only in the band gaps and the band widths, but not in the characteristics of self-similarity and the Cantor set.Comment: 13 pages, 5 Postscript figure

Local dissipation effects in two-dimensional quantum Josephson junction arrays with magnetic field

We study the quantum phase transitions in two-dimensional arrays of Josephson-couples junctions with short range Josephson couplings (given by the Josephson energy) and the charging energy. We map the problem onto the solvable quantum generalization of the spherical model that improves over the mean-field theory method. The arrays are placed on the top of a two-dimensional electron gas separated by an insulator. We include effects of the local dissipation in the presence of an external magnetic flux f in square lattice for several rational fluxes f=0,1/2,1/3,1/4 and 1/6. We also have examined the T=0 superconducting-insulator phase boundary as function of a dissipation alpha for two different geometry of the lattice: square and triangular. We have found critical value of the dissipation parameter independent on geometry of the lattice and presence magnetic field.Comment: accepted to PR

A Note on Solid-State Maxwell Demon

Starting from 2002, at least two kinds of laboratory-testable, solid-state Maxwell demons have been proposed that utilize the electric field energy of an open-gap n-p junction and that seem to challenge the validity of the Second Law of Thermodynamics. In the present paper we present some arguments against the alleged functioning of such devices.Comment: 9 pages, 4 figures. Foundations of Physics, forthcoming. arXiv admin note: substantial text overlap with arXiv:1101.505

Area versus Length Distribution for Closed Random Walks

Using a connection between the $q$-oscillator algebra and the coefficients of the high temperature expansion of the frustrated Gaussian spin model, we derive an exact formula for the number of closed random walks of given length and area, on a hypercubic lattice, in the limit of infinite number of dimensions. The formula is investigated in detail, and asymptotic behaviours are evaluated. The area distribution in the limit of long loops is computed. As a byproduct, we obtain also an infinite set of new, nontrivial identities.Comment: 17 page

Ground-simulation investigations of VTOL airworthiness criteria for terminal-area operations

Several ground-based simulation experiments undertaken to investigate concerns related to tilt-rotor aircraft airworthiness were conducted. The experiments were conducted on the National Aeronautics and Space Administration (NASA) Ames Research Center's Vertical Motion Simulator, which permits simulation of a wide variety of aircraft with a high degree of fidelity of motion cueing. Variations in conversion/deceleration profile, type of augmentation or automation, level of display assistance, and meteorological conditions were considered in the course of the experiments. Certification pilots from the Federal Aviation Administration (FAA) and the Civil Aviation Authority (CAA) participated, in addition to NASA research pilots. The setup of these experiments on the simulator is summarized, and some of the results highlighted