A numerical finite size scaling approach to many-body localization

We develop a numerical technique to study Anderson localization in interacting electronic systems. The ground state of the disordered system is calculated with quantum Monte-Carlo simulations while the localization properties are extracted from the ``Thouless conductance'' $g$, i.e. the curvature of the energy with respect to an Aharonov-Bohm flux. We apply our method to polarized electrons in a two dimensional system of size $L$. We recover the well known universal $\beta(g)=\rm{d}\log g/\rm{d}\log L$ one parameter scaling function without interaction. Upon switching on the interaction, we find that $\beta(g)$ is unchanged while the system flows toward the insulating limit. We conclude that polarized electrons in two dimensions stay in an insulating state in the presence of weak to moderate electron-electron correlations.Comment: 5 pages, 4 figure

A model of gravitation with global U(1)-symmetry

It is shown that an embedding of the general relativity $4-$space into a flat $12-$space gives a model of gravitation with the global $U(1)-$symmetry and the discrete $D_{1}-$one. The last one may be transformed into the $SU(2)-$symmetry of the unified model, and the demand of independence of $U(1)-$ and $SU(2)-$transformations leads to the estimate $\sin^{2}\theta_{min}=0,20$ where $\theta_{min}$ is an analog of the Weinberg angle of the standard model.Comment: 7 page

Fractional Supersymmetry and Fth-Roots of Representations

A generalization of super-Lie algebras is presented. It is then shown that all known examples of fractional supersymmetry can be understood in this formulation. However, the incorporation of three dimensional fractional supersymmetry in this framework needs some care. The proposed solutions lead naturally to a formulation of a fractional supersymmetry starting from any representation D of any Lie algebra g. This involves taking the Fth-roots of D in an appropriate sense. A fractional supersymmetry in any space-time dimension is then possible. This formalism finally leads to an infinite dimensional extension of g, reducing to the centerless Virasoro algebra when g=sl(2,R).Comment: 23 pages, 1 figure, LaTex file with epsf.st

The energy scale behind the metallic behaviors in low-density Si-MOSFETs

We show that the unexpected metallic behavior (the so-called two-dimensional metal-insulator transition) observed in low-density Silicon metal-oxide-semiconductor field-effect transistors (Si-MOSFETs) is controlled by a unique characteristic energy scale, the polarization energy. On one hand, we perform Quantum Monte Carlo calculations of the energy needed to polarize the two dimensional electron gas at zero temperature, taking into account Coulomb interactions, valley degeneracy and electronic mobility (disorder). On the other hand, we identify the characteristic energy scale controlling the physics in eight different sets of experiments. We find that our {\it ab-initio} polarization energies (obtained without any adjustable parameters) are in perfect agreement with the observed characteristic energies for all available data, both for the magnetic field and temperature dependence of the resistivities. Our results put strong constraints on possible mechanisms responsible for the metallic behavior. In particular, there are strong indications that the system would eventually become insulating at low enough temperature.Comment: two references added, corrected typos, minor changes, final version as publishe

Do metals exist in two dimensions? A study of many-body localisation in low density electron gas

Using a combination of ground state quantum Monte-Carlo and finite size scaling techniques, we perform a systematic study of the effect of Coulomb interaction on the localisation length of a disordered two-dimensional electron gas. We find that correlations delocalise the 2D system. In the absence of valley degeneracy (as in GaAs heterostructures), this delocalization effect corresponds to a finite increase of the localization length. The delocalisation is much more dramatic in the presence of valley degeneracy (as in Si MOSFETSs) where the localization length increases drastically. Our results suggest that a rather simple mechanism can account for the main features of the metallic behaviour observed in high mobility Si MOSFETs. Our findings support the claim that this behaviour is indeed a genuine effect of the presence of electron-electron interactions, yet that the system is not a ``true'' metal in the thermodynamic sense.Comment: 5 pages 4 figure

On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry

We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation or the trivial representation. We use these results to show that every orthosupersymmetric system of order $p$ has a parasupersymmetry of order $p$ and a fractional supersymmetry of order $p+1$.Comment: 13 pages, to appear in J. Phys. A: Math. Ge

Marqueurs diagnostics des scédosporioses : Catalase cytosolique et/ou excrétée

National audienc

On a graded q-differential algebra

Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differential algebra in the case of a reduced quantum plane which can be endowed with a structure of a graded algebra. We consider the differential d satisfying d to power N equals zero as an analog of an exterior differential and study the first order differential calculus induced by this differential.Comment: 6 pages, submitted to the Proceedings of the "International Conference on High Energy and Mathematical Physics", Morocco, Marrakech, April 200

Towards a standardized test for serodiagnosis of scedosporiosis

International audienc