Suppression of compressible edge channels and spatial spin polarization in the integer quantum Hall regime

We perform systematic numerical studies of the structure of spin-resolved compressible strips in split-gate quantum wires taking into account the exchange and correlation interactions within the density functional theory in the local spin-density approximation. We find that for realistic parameters of the wire the exchange interaction can completely suppress the formation of the compressible strips. As the depletion length or magnetic field are increased, the compressible strips starts to form first for the spin-down and then for spin-up edge channels. We demonstrate that the widths of these strips plus the spatial separation between them caused by the exchange interaction are equal to the width of the compressible strip calculated in the Hartree approximation for spinless electrons. We also discuss the effect of electron density on the suppression of the compressible strips in quantum wires.Comment: 5 pages, 4 figures, submitted to Phys. Rev.

Massless and massive one-loop three-point functions in negative dimensional approach

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of external momenta (and masses for the massive cases) where the propagators in the Feynman integrals are raised to arbitrary exponents and the dimension of the space-time D. Our approach reproduces the known results as well as other solutions as yet unknown in the literature. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories

Quantum walks with an anisotropic coin I: spectral theory

We perform the spectral analysis of the evolution operator U of quantum walks with an anisotropic coin, which include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. In particular, we determine the essential spectrum of U, we show the existence of locally U-smooth operators, we prove the discreteness of the eigenvalues of U outside the thresholds, and we prove the absence of singular continuous spectrum for U. Our analysis is based on new commutator methods for unitary operators in a two-Hilbert spaces setting, which are of independent interest.Comment: 26 page

Implications of a new light gauge boson for neutrino physics

We study the impact of light gauge bosons on neutrino physics. We show that they can explain the NuTeV anomaly and also escape the constraints from neutrino experiments if they are very weakly coupled and have a mass of a few GeV. Lighter gauge bosons with stronger couplings could explain both the NuTeV anomaly and the positive anomalous magnetic moment of the muon. However, in the simple model we consider in this paper (say a purely vectorial extra U(1) current), they appear to be in conflict with the precise measurements of \nu-e elastic scattering cross sections. The surprising agreement that we obtain between our naive model and the NuTeV anomaly for a Z' mass of a few GeV may be a coincidence. However, we think it is interesting enough to deserve attention and perhaps a more careful analysis, especially since a new light gauge boson is a very important ingredient for the Light Dark Matter scenario.Comment: 9 page

The dilute A_L models and the integrable perturbations of unitary minimal CFTs

Recently, a set of thermodynamic Bethe ansatz equations is proposed by Dorey, Pocklington and Tateo for unitary minimal models perturbed by \phi_{1,2} or \phi_{2,1} operator. We examine their results in view of the lattice analogues, dilute A_L models at regime 1 and 2. Taking M_{5,6}+\phi_{1,2} and M_{3,4}+\phi_{2,1} as the simplest examples, we will explicitly show that the conjectured TBA equations can be recovered from the lattice model in a scaling limit.Comment: 14 pages, 2 figure

Vacuum type of SU(2) gluodynamics in maximally Abelian and Landau gauges

The vacuum type of SU(2) gluodynamics is studied using Monte-Carlo simulations in maximally Abelian (MA) gauge and in Landau (LA) gauge, where the dual Meissner effect is observed to work. The dual Meissner effect is characterized by the coherence and the penetration lengths. Correlations between Wilson loops and electric fields are evaluated in order to measure the penetration length in both gauges. The coherence length is shown to be fixed in the MA gauge from measurements of the monopole density around the static quark-antiquark pair. It is also shown numerically that a dimension 2 gluon operator A^+A^-(s) and the monopole density has a strong correlation as suggested theoretically. Such a correlation is observed also between the monopole density and A^2(s)= A^+A^-(s) + A^3A^3(s) condensate if the remaining U(1) gauge degree of freedom is fixed to U(1) Landau gauge (U1LA). The coherence length is determined numerically also from correlations between Wilson loops and A^+A^-(s) and A^2(s) in MA + U1LA gauge. Assuming that the same physics works in the LA gauge, we determine the coherence length from correlations between Wilson loops and A^2(s). Penetration lengths and coherence lengths in the two gauges are almost the same. The vacuum type of the confinement phase in both gauges is near to the border between the type 1 and the type 2 dual superconductors.Comment: 13 pages, 22 figures, RevTeX 4 styl

Fourth Order Algorithms for Solving the Multivariable Langevin Equation and the Kramers Equation

We develop a fourth order simulation algorithm for solving the stochastic Langevin equation. The method consists of identifying solvable operators in the Fokker-Planck equation, factorizing the evolution operator for small time steps to fourth order and implementing the factorization process numerically. A key contribution of this work is to show how certain double commutators in the factorization process can be simulated in practice. The method is general, applicable to the multivariable case, and systematic, with known procedures for doing fourth order factorizations. The fourth order convergence of the resulting algorithm allowed very large time steps to be used. In simulating the Brownian dynamics of 121 Yukawa particles in two dimensions, the converged result of a first order algorithm can be obtained by using time steps 50 times as large. To further demostrate the versatility of our method, we derive two new classes of fourth order algorithms for solving the simpler Kramers equation without requiring the derivative of the force. The convergence of many fourth order algorithms for solving this equation are compared.Comment: 19 pages, 2 figure

One-loop N-point equivalence among negative-dimensional, Mellin-Barnes and Feynman parametrization approaches to Feynman integrals

We show that at one-loop order, negative-dimensional, Mellin-Barnes' (MB) and Feynman parametrization (FP) approaches to Feynman loop integrals calculations are equivalent. Starting with a generating functional, for two and then for $N$-point scalar integrals we show how to reobtain MB results, using negative-dimensional and FP techniques. The $N-$point result is valid for different masses, arbitrary exponents of propagators and dimension.Comment: 11 pages, LaTeX. To be published in J.Phys.