Contact, the feature pool and the speech community : The emergence of Multicultural London English.

In Northern Europe’s major cities, new varieties of the host languages are emerging in the multilingual inner cities. While some analyse these ‘multiethnolects’ as youth styles, we take a variationist approach to an emerging ‘Multicultural London English’ (MLE), asking: (1) what features characterise MLE? (2) at what age(s) are they acquired? (3) is MLE vernacularised? (4) when did MLE emerge, and what factors enabled its emergence? We argue that innovations in the diphthongs and the quotative system are generated from the specific sociolinguistics of inner-city London, where at least half the population is undergoing group second-language acquisition and where high linguistic diversity leads to a feature pool to select from. We look for incrementation (Labov) in the acquisition of the features, but find this only for two ‘global’ changes, BE LIKE and GOOSE-fronting, for which adolescents show the highest usage. Community-internal factors explain the age-related variation in the remaining features

Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops

We consider two coupled quantum tops with angular momentum vectors $\mathbf{L}$ and $\mathbf{M}$. The coupling Hamiltonian defines the Feinberg-Peres model which is a known paradigm of quantum chaos. We show that this model has a nonstandard symmetry with respect to the Altland-Zirnbauer tenfold symmetry classification of quantum systems which extends the well-known threefold way of Wigner and Dyson (referred to as `standard' symmetry classes here). We identify that the nonstandard symmetry classes BD$I_0$ (chiral orthogonal class with no zero modes), BD$I_1$ (chiral orthogonal class with one zero mode) and C$I$ (antichiral orthogonal class) as well as the standard symmetry class A$I$ (orthogonal class). We numerically analyze the specific spectral quantum signatures of chaos related to the nonstandard symmetries. In the microscopic density of states and in the distribution of the lowest positive energy eigenvalue we show that the Feinberg-Peres model follows the predictions of the Gaussian ensembles of random-matrix theory in the appropriate symmetry class if the corresponding classical dynamics is chaotic. In a crossover to mixed and near-integrable classical dynamics we show that these signatures disappear or strongly change.Comment: 15 page

Axiomatics for the external numbers of nonstandard analysis

Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is the algebraic sum of a nonstandard real number and a neutrix. Due to the stability by some shifts, external numbers may be seen as mathematical models for orders of magnitude. The algebraic properties of external numbers gave rise to the so-called solids, which are extensions of ordered fields, having a restricted distributivity law. However, necessary and sufficient conditions can be given for distributivity to hold. In this article we develop an axiomatics for the external numbers. The axioms are similar to, but mostly somewhat weaker than the axioms for the real numbers and deal with algebraic rules, Dedekind completeness and the Archimedean property. A structure satisfying these axioms is called a complete arithmetical solid. We show that the external numbers form a complete arithmetical solid, implying the consistency of the axioms presented. We also show that the set of precise elements (elements with minimal magnitude) has a built-in nonstandard model of the rationals. Indeed the set of precise elements is situated between the nonstandard rationals and the nonstandard reals whereas the set of non-precise numbers is completely determined