Projection on higher Landau levels and non-commutative geometry

The projection of a two dimensional planar system on the higher Landau levels of an external magnetic field is formulated in the language of the non commutative plane and leads to a new class of star products.Comment: 12 pages, latex, corrected versio

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

Geometric extensions of many-particle Hardy inequalities

Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy inequalities to involve volumes of simplices spanned by a subset of points. Clifford/multilinear algebra is employed to simplify geometric computations. These results and the techniques involved are relevant for classes of exactly solvable quantum systems such as the Calogero-Sutherland models and their higher-dimensional generalizations, as well as for membrane matrix models, and models of more complicated particle interactions of geometric character.Comment: Revised version. 28 page

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

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

Symmetries of topological field theories in the BV-framework

Topological field theories of Schwarz-type generally admit symmetries whose algebra does not close off-shell, e.g. the basic symmetries of BF models or vector supersymmetry of the gauge-fixed action for Chern-Simons theory (this symmetry being at the origin of the perturbative finiteness of the theory). We present a detailed discussion of all these symmetries within the algebraic approach to the Batalin-Vilkovisky formalism. Moreover, we discuss the general algebraic construction of topological models of both Schwarz- and Witten-type.Comment: 30 page

Geometric Exponents, SLE and Logarithmic Minimal Models

In statistical mechanics, observables are usually related to local degrees of freedom such as the Q < 4 distinct states of the Q-state Potts models or the heights of the restricted solid-on-solid models. In the continuum scaling limit, these models are described by rational conformal field theories, namely the minimal models M(p,p') for suitable p, p'. More generally, as in stochastic Loewner evolution (SLE_kappa), one can consider observables related to nonlocal degrees of freedom such as paths or boundaries of clusters. This leads to fractal dimensions or geometric exponents related to values of conformal dimensions not found among the finite sets of values allowed by the rational minimal models. Working in the context of a loop gas with loop fugacity beta = -2 cos(4 pi/kappa), we use Monte Carlo simulations to measure the fractal dimensions of various geometric objects such as paths and the generalizations of cluster mass, cluster hull, external perimeter and red bonds. Specializing to the case where the SLE parameter kappa = 4p'/p is rational with p < p', we argue that the geometric exponents are related to conformal dimensions found in the infinitely extended Kac tables of the logarithmic minimal models LM(p,p'). These theories describe lattice systems with nonlocal degrees of freedom. We present results for critical dense polymers LM(1,2), critical percolation LM(2,3), the logarithmic Ising model LM(3,4), the logarithmic tricritical Ising model LM(4,5) as well as LM(3,5). Our results are compared with rigourous results from SLE_kappa, with predictions from theoretical physics and with other numerical experiments. Throughout, we emphasize the relationships between SLE_kappa, geometric exponents and the conformal dimensions of the underlying CFTs.Comment: Added reference

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

Off-diagonal correlations in one-dimensional anyonic models: A replica approach

We propose a generalization of the replica trick that allows to calculate the large distance asymptotic of off-diagonal correlation functions in anyonic models with a proper factorizable ground-state wave-function. We apply this new method to the exact determination of all the harmonic terms of the correlations of a gas of impenetrable anyons and to the Calogero Sutherland model. Our findings are checked against available analytic and numerical results.Comment: 19 pages, 5 figures, typos correcte

Controls on Ice Cliff Distribution and Characteristics on Debris-Covered Glaciers

Ice cliff distribution plays a major role in determining the melt of debris-covered glaciers but its controls are largely unknown. We assembled a data set of 37,537 ice cliffs and determined their characteristics across 86 debris-covered glaciers within High Mountain Asia (HMA). We find that 38.9% of the cliffs are stream-influenced, 19.5% pond-influenced and 19.7% are crevasse-originated. Surface velocity is the main predictor of cliff distribution at both local and glacier scale, indicating its dependence on the dynamic state and hence evolution stage of debris-covered glacier tongues. Supraglacial ponds contribute to maintaining cliffs in areas of thicker debris, but this is only possible if water accumulates at the surface. Overall, total cliff density decreases exponentially with debris thickness as soon as the debris layer reaches a thickness of over 10 cm