Transport Properties and Density of States of Quantum Wires with Off-diagonal Disorder

We review recent work on the random hopping problem in a quasi-one-dimensional geometry of N coupled chains (quantum wire with off-diagonal disorder). Both density of states and conductance show a remarkable dependence on the parity of N. The theory is compared to numerical simulations.Comment: 8 pages, to appear in Physica E (special issue on Dynamics of Complex Systems); 6 figure

Anderson localization and the topology of classifying spaces

We construct the generic phase diagrams encoding the topologically distinct localized and delocalized phases of noninteracting fermionic quasiparticles for any symmetry class from the tenfold way in one, two, and three dimensions. To this end, we start from a massive Dirac Hamiltonian perturbed by a generic disorder for any dimension of space and for any one of the ten symmetry classes from the tenfold way. The physics of Anderson localization is then encoded by a two-dimensional phase diagram that we deduce from the topology of the space of normalized Dirac masses. This approach agrees with previously known results and gives an alternative explanation for the even-odd effect in the one-dimensional chiral symmetry classes. We also give a qualitative explanation for the Gade singularity and Griffiths effects in the density of states using the first homotopy group of the normalized Dirac masses in two dimensions. Finally, this approach is used to analyze the stability of massless Dirac fermions on the surface of three-dimensional topological crystalline insulators.Comment: 45 pages, 6 figure

Ground state degeneracy of non-Abelian topological phases from coupled wires

We construct a family of two-dimensional non-Abelian topological phases from coupled wires using a non-Abelian bosonization approach. We then demonstrate how to determine the nature of the non-Abelian topological order (in particular, the anyonic excitations and the topological degeneracy on the torus) realized in the resulting gapped phases of matter. This paper focuses on the detailed case study of a coupled-wire realization of the bosonic $su(2)^{\,}_{2}$ Moore-Read state, but the approach we outline here can be extended to general bosonic $su(2)^{\,}_{k}$ topological phases described by non-Abelian Chern-Simons theories. We also discuss possible generalizations of this approach to the construction of three-dimensional non-Abelian topological phases.Comment: 33 pages, 3 figures. v3 replaces previous discussion of 3D case with an outlook. Published versio

Electron fractionalization in two-dimensional graphenelike structures

Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. In this letter, we show that fractionally charged topological excitations exist on graphenelike structures, where quasiparticles are described by two flavors of Dirac fermions and time-reversal symmetry is respected. The topological zero-modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics.Comment: 4 pages, 2 figure

Density of states in coupled chains with off-diagonal disorder

We compute the density of states (d.o.s.) in N coupled chains with random hopping. At zero energy, the d.o.s. shows a singularity that strongly depends on the parity of N. For odd N, the d.o.s. is proportional to 1/(E (\ln |E|)^3), with and without time-reversal symmetry. For even N, the d.o.s. is proportional to \ln |E| in the presence of time-reversal symmetry, while there is a pseudogap, d.o.s. proportional to E \ln |E|, in the absence of time-reversal symmetry.Comment: 4 pages, RevTeX; 3 figures included with eps

L'analyse discriminante, un puissant moyen de validation des hypothèses hydrogéologiques

L'étude des tableaux de données hydrochimiques acquises au cours de campagnes synchrones (« instantanés ») ou de suivis diachroniques à pas régulier (hebdomadaire, quotidien, horaire) s'opère généralement en résumant l'information par des méthodes statistiques. Ces méthodes descriptives, qui négligent nécessairement une partie de l'information initiale, permettent l'interprétation de la structure du tableau de données en termes de fonctionnement hydrocinématique (BAKALOWICZ, 1979, 1982, MUDRY et BLAVOUX, 1988, ROLET et SEGUIN, 1986 8 et b).Ces méthodes, fondées sur l'analyse d'une seule population statistique (bi ou multidimensionnelle) impliquent un mode de raisonnement déductif.Leur application, ainsi que l'examen du tableau des données brutes (ou de ses représentations graphiques), peut mettre en évidence des sous-groupes fondés sur des critères hydrogéologiques. La réalité de ces sous-groupes peut être testée à l'aide de méthodes statistiques basées sur l'analyse de la variance. Certaines méthodes utilisent le rapport des variances qu'elles comparent à la distribution de Snedecor (analyse de la variance à une ou deux voies), d'autres comparent des variances multidimensionnelles intraclasses à la variance interclasses, c'est le cas de l'analyse discriminante. Les sous-groupes constituent une variable qualitative dont la pertinence peut être démontrée par la calcul. L'analyse discriminante apparaît donc comme un outil décisionnel. Le présent article présente brièvement la méthode du point de vue statistique et montre deux exemples d'application à des sources karstiques.Le premier exemple traite de l'appartenance chimique d'une phase de basses eaux à la petite crue qui la précède et non à un tarissement au sens hydrocinématique. L'analyse discriminante permet d'affirmer qu'une recharge peu perceptible sur l'hydrogramme de la source amène une évolution chimique irréversible de l'eau de la réserve, responsable des phénomènes d'hystérésis observés sur les courbes concentration-débit. Ce cas est celui de l'aquifère de la Fontaine de Vaucluse (Sud-Est de la France) pendant un suivi quotidien d'étiage.Le second exemple permet de rattacher, par son comportement physico-chimique hebdomadaire, une émergence karstique à une autre et non à une troisième. Ce cas est celui du karst de la Rochefoucauld (Charente), avec les sources du Bouillant, de la Font de Lussac et de la Lèche. Les sources du Bouillant et de la Font de Lussac ont un comportement physico-chimique semblable, alors que la Lèche réagit de manière totalement indépendante. Elle constitue un système globalement distinct du point de vue hydrocinématique, ce qui permet de minimiser les relations mises en évidence par traçage artificiel entre les deux systèmes.The study of the hydrochemical data tables obtained during synchronous sampling (weekly, daily or hourly) is generally carried out by resuming the information by statistical methods. These methods, that disregard part of the initial information, allow to explain the structure of the data table in terms of hydrokinematics (BAKALOWICZ, 1979, 1982; MUDRY et BLAVOUX, 1986; ROLET et SEGUIN, 1986 a et b).These descriptive methods, based on the analysis of a single (bi or multivariate) statistical population, imply deductive reasoning. Their application, as well as the study of the untreated data table (or of its scattergrams), can show the presence of sub-groups based on hydrogeological criteria. The existence of such sub-groups can be tested by statistical methods based on variance analysis. Several methods use the variance ratio and compare it to Snedecor's distribution (single or double path variance analysis), others compare multidimensional intragroup variances to intergroup variance. This is the case with discriminant analysis.This paper describes the method from a point of view of statistics and presents two examples of application to karst springs.The first study deals with the chemical relationship of a low-water period with the preceding period of small floods and not to a hydrokinematical water drying up. The discriminant analysis allows to say Chat a recharge less visible on the hydrograph of the spring induces a non reversible chemical evolution of the reserve water. This is the case of the Fontaine de Vaucluse karst spring (Southeastern France) during a daily low water sampling.The second study allows to relate a karst spring to another one, thanks to its weekly physico-chemical behaviour, and not to a third one : this is the case of the La Rochefoucauld karst system (Charente, Western France) with the Bouillant, Font de Lussac and Lèche springs. The Bouillant and Font de Lussac springs behave in the same way hydrochemically, whereas the Lèche works independently. It is, hydrokinematically, a separate karst system, even if there is a certain relationship between all of them

L'énigme de la 3e satire de Juvenal

pp.165-174Nella terza satira di Giovenale, Umbricio, dopo una lunga tirata contro i Greci, decide di fuggire da Roma, ormai invasa dall’immigrazione greca, e intende stranamente stabilirsi a Cuma, che è la più antica colonia greca in Italia. Ma Umbricio non rigetta la cultura greca, solo l’invasione greca a Roma. Per questo il suo esilio volontario in un’isola greca ormai vacua, e vicina ad Aquino, patria di Giovenale, baluardo dell’autenticità romana, riunirà da una parte una Grecia non contaminata dagli affaristi emigrati a Roma, dall’altra una Roma fedele alle sue tradizioni e alla sua identità profonda.In the third satire of Juvenal, Umbricius, after a long tirade against the Greeks, decides to flee Rome, now invaded by Greek immigrates. Nevertheless, strangely enough, he wants to settle in Cumae, the most ancient Greek colony in Italy. But Umbricius does not reject Greek culture, he just does not feel at ease in the newly invaded city. Hence his voluntary exile in a Greek island, now uacua: it was located next to Aquinum, the birthplace of Juvenal, a bastion of Romanitas and will reunite, on the one hand, a Greece still not polluted by businessmen emigrated to Rome, and, on the other, a Rome which is still faithful to its traditions and its profound identity

Nonuniversality in quantum wires with off-diagonal disorder: a geometric point of view

It is shown that, in the scaling regime, transport properties of quantum wires with off-diagonal disorder are described by a family of scaling equations that depend on two parameters: the mean free path and an additional continuous parameter. The existing scaling equation for quantum wires with off-diagonal disorder [Brouwer et al., Phys. Rev. Lett. 81, 862 (1998)] is a special point in this family. Both parameters depend on the details of the microscopic model. Since there are two parameters involved, instead of only one, localization in a wire with off-diagonal disorder is not universal. We take a geometric point of view and show that this nonuniversality follows from the fact that the group of transfer matrices is not semi-simple. Our results are illustrated with numerical simulations for a tight-binding model with random hopping amplitudes.Comment: 12 pages, RevTeX; 3 figures included with eps