Random Aharonov-Bohm vortices and some funny families of integrals

A review of the random magnetic impurity model, introduced in the context of the integer Quantum Hall effect, is presented. It models an electron moving in a plane and coupled to random Aharonov-Bohm vortices carrying a fraction of the quantum of flux. Recent results on its perturbative expansion are given. In particular, some funny families of integrals show up to be related to the Riemann $\zeta(3)$ and $\zeta(2)$.Comment: 10 page

Hall Conductivity for Two Dimensional Magnetic Systems

A Kubo inspired formalism is proposed to compute the longitudinal and transverse dynamical conductivities of an electron in a plane (or a gas of electrons at zero temperature) coupled to the potential vector of an external local magnetic field, with the additional coupling of the spin degree of freedom of the electron to the local magnetic field (Pauli Hamiltonian). As an example, the homogeneous magnetic field Hall conductivity is rederived. The case of the vortex at the origin is worked out in detail. This system happens to display a transverse Hall conductivity ($P$ breaking effect) which is subleading in volume compared to the homogeneous field case, but diverging at small frequency like $1/\omega^2$. A perturbative analysis is proposed for the conductivity in the random magnetic impurity problem (Poissonian vortices in the plane). At first order in perturbation theory, the Hall conductivity displays oscillations close to the classical straight line conductivity of the mean magnetic field.Comment: 28 pages, latex, 2 figure

On a different BRST constructions for a given Lie algebra

The method of the BRST quantization is considered for the system of constraints, which form a Lie algebra. When some of the Cartan generators do not imply any conditions on the physical states, the system contains the first and the second class constraints. After the introduction auxiliary bosonic degrees of freedom for these cases, the corresponding BRST charges with the nontrivial structure of nonlinear terms in ghosts are constructed.Comment: 10 Pages, LaTe

Persistent Current of Free Electrons in the Plane

Predictions of Akkermans et al. are essentially changed when the Krein spectral displacement operator is regularized by means of zeta function. Instead of piecewise constant persistent current of free electrons on the plane one has a current which varies linearly with the flux and is antisymmetric with regard to all time preserving values of $\alpha$ including $1/2$. Different self-adjoint extensions of the problem and role of the resonance are discussed.Comment: (Comment on "Relation between Persistent Currents and the Scattering Matrix", Phys. Rev. Lett. {\bf 66}, 76 (1991)) plain latex, 4pp., IPNO/TH 94-2

Area distribution of two-dimensional random walks on a square lattice

The algebraic area probability distribution of closed planar random walks of length N on a square lattice is considered. The generating function for the distribution satisfies a recurrence relation in which the combinatorics is encoded. A particular case generalizes the q-binomial theorem to the case of three addends. The distribution fits the L\'evy probability distribution for Brownian curves with its first-order 1/N correction quite well, even for N rather small.Comment: 8 pages, LaTeX 2e. Reformulated in terms of q-commutator

Direct sequence spread spectrum sequences

DS-CDMA (for Direct-Sequence Code-Division Multiple-Access, in english, or AMRC, for Accès Multiple à Répartition par les Codes, in french) receivers are significantly performance degraded by the non-orthogonality of the classicaly used spreading sequences, mainly because of the odd correlation functions . The "Tabu Search" algorithm enables sequence generation optimising various criteria . The obtained performance are better than those of the Litterature . Moreover, the proposed method enables the optimisation of sequence sets of any desired length and cardinal, what is not the case for the previous mathematically constructed sequences .Les récepteurs DS-CDMA (pour Direct-Sequence Code-Division Multiple-Access, en anglais, ou AMRC, pour Accès Multiple à Répartition par les Codes, en français) voient leur performance être dégradée de manière significative par la non-orthogonalité des séquences d'étalement classiquement utilisées et principalement à cause des fonctions de corrélation impaires. L'algorithme dit de « Recherche Taboue » (ou Tabu Search, en anglais) permet la génération de séquences optimisant différents critères. Les performances obtenues sont meilleures que celles des séquences de la littérature. De plus, la démarche exposée permet d'optimiser des jeux de séquences de longueur et de cardinal quelconques, ce qui n'est pas le cas des séquences construites de manière mathématique

Finite-size anyons and perturbation theory

We address the problem of finite-size anyons, i.e., composites of charges and finite radius magnetic flux tubes. Making perturbative calculations in this problem meets certain difficulties reminiscent of those in the problem of pointlike anyons. We show how to circumvent these difficulties for anyons of arbitrary spin. The case of spin 1/2 is special because it allows for a direct application of perturbation theory, while for any other spin, a redefinition of the wave function is necessary. We apply the perturbative algorithm to the N-body problem, derive the first-order equation of state and discuss some examples.Comment: 18 pages (RevTex) + 4 PS figures (all included); a new section on equation of state adde

Universal Hidden Supersymmetry in Classical Mechanics and its Local Extension

We review here a path-integral approach to classical mechanics and explore the geometrical meaning of this construction. In particular we bring to light a universal hidden BRS invariance and its geometrical relevance for the Cartan calculus on symplectic manifolds. Together with this BRS invariance we also show the presence of a universal hidden genuine non-relativistic supersymmetry. In an attempt to understand its geometry we make this susy local following the analogous construction done for the supersymmetric quantum mechanics of Witten.Comment: 6 pages, latex, Volkov Memorial Proceeding

Classical limit for the scattering of Dirac particles in a magnetic field

We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by a solenoidal magnetic field. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non relativistic case. We show that taking pr_0\|sin(\theta/2)|/\hbar<<1 in our expression of the differential cross section it reduces to the one reported by AB, and if additionally we assume \theta << 1 our result becomes the one obtained by LL. However, these limits are explicitly singular in \hbar as opposed to our initial result. We analyze the singular behavior in \hbar and show that the perturbative Planck's limit (\hbar -> 0) is consistent, contrarily to those of the AB and LL expressions. We also discuss the scattering in a uniform and constant magnetic field, which resembles some features of QCD

Conductance and Shot Noise for Particles with Exclusion Statistics

The first quantized Landauer approach to conductance and noise is generalized to particles obeying exclusion statistics. We derive an explicit formula for the crossover between the shot and thermal noise limits and argue that such a crossover can be used to determine experimentally whether charge carriers in FQHE devices obey exclusion statistics.Comment: 4 pages, revtex, 1 eps figure include