Diffusion of Dirac fermions across a topological merging transition in two dimensions

A continuous deformation of a Hamiltonian possessing at low energy two Dirac points of opposite chiralities can lead to a gap opening by merging of the two Dirac points. In two dimensions, the critical Hamiltonian possesses a semi-Dirac spectrum: linear in one direction but quadratic in the other. We study the transport properties across such a transition, from a Dirac semi-metal through a semi-Dirac phase towards a gapped phase. Using both a Boltzmann approach and a diagrammatic Kubo approach, we describe the conductivity tensor within the diffusive regime. In particular, we show that both the anisotropy of the Fermi surface and the Dirac nature of the eigenstates combine to give rise to anisotropic transport times, manifesting themselves through an unusual matrix self-energy.Comment: 15 pages, 14 figure

Dephasing by a nonstationary classical intermittent noise

We consider a new phenomenological model for a $1/f^{\mu}$ classical intermittent noise and study its effects on the dephasing of a two-level system. Within this model, the evolution of the relative phase between the $|\pm>$ states is described as a continuous time random walk (CTRW). Using renewal theory, we find exact expressions for the dephasing factor and identify the physically relevant various regimes in terms of the coupling to the noise. In particular, we point out the consequences of the non-stationarity and pronounced non-Gaussian features of this noise, including some new anomalous and aging dephasing scenarii.Comment: Submitted to Phys. Rev.

Renormalization of modular invariant Coulomb gas and Sine-Gordon theories, and quantum Hall flow diagram

Using the renormalisation group (RG) we study two dimensional electromagnetic coulomb gas and extended Sine-Gordon theories invariant under the modular group SL(2,Z). The flow diagram is established from the scaling equations, and we derive the critical behaviour at the various transition points of the diagram. Following proposal for a SL(2,Z) duality between different quantum Hall fluids, we discuss the analogy between this flow and the global quantum Hall phase diagram.Comment: 10 pages, 1 EPS figure include

Rational matrix pseudodifferential operators

The skewfield K(d) of rational pseudodifferential operators over a differential field K is the skewfield of fractions of the algebra of differential operators K[d]. In our previous paper we showed that any H from K(d) has a minimal fractional decomposition H=AB^(-1), where A,B are elements of K[d], B is non-zero, and any common right divisor of A and B is a non-zero element of K. Moreover, any right fractional decomposition of H is obtained by multiplying A and B on the right by the same non-zero element of K[d]. In the present paper we study the ring M_n(K(d)) of nxn matrices over the skewfield K(d). We show that similarly, any H from M_n(K(d)) has a minimal fractional decomposition H=AB^(-1), where A,B are elements of M_n(K[d]), B is non-degenerate, and any common right divisor of A and B is an invertible element of the ring M_n(K[d]). Moreover, any right fractional decomposition of H is obtained by multiplying A and B on the right by the same non-degenerate element of M_n(K [d]). We give several equivalent definitions of the minimal fractional decomposition. These results are applied to the study of maximal isotropicity property, used in the theory of Dirac structures.Comment: 20 page

On the relevance of polyynyl-substituted PAHs to astrophysics

We report on the absorption spectra of the polycyclic aromatic hydrocarbon (PAH) molecules anthracene, phenanthrene, and pyrene carrying either an ethynyl (-C2H) or a butadiynyl (-C4H) group. Measurements were carried out in the mid infrared at room temperature on grains embedded in CsI pellets and in the near ultraviolet at cryogenic temperature on molecules isolated in Ne matrices. The infrared measurements show that interstellar populations of polyynyl-substituted PAHs would give rise to collective features in the same way non-substituted PAHs give rise to the aromatic infrared bands. The main features characteristic of the substituted molecules correspond to the acetylenic CH stretching mode near 3.05 mum and to the almost isoenergetic acetylenic CCH in- and out-of-plane bending modes near 15.9 mum. Sub-populations defined by the length of the polyynyl side group cause collective features which correspond to the various acetylenic CC stretching modes. The ultraviolet spectra reveal that the addition of an ethynyl group to a non-substituted PAH molecule results in all its electronic transitions being redshifted. Due to fast internal energy conversion, the bands at shorter wavelengths are significantly broadened. Those at longer wavelengths are only barely affected in this respect. As a consequence, their relative peak absorption increases. The substitution with the longer butadiynyl chain causes the same effects with a larger magnitude, resulting in the spectra to show a prominent if not dominating pi-pi* transition at long wavelength. After discussing the relevance of polyynyl-substituted PAHs to astrophysics, we conclude that this class of highly conjugated, unsaturated molecules are valid candidates for the carriers of the diffuse interstellar bands.Comment: 29 pages, 9 figures, accepted for publication in ApJ 2 April 201

Cross-Over between universality classes in a magnetically disordered metallic wire

In this article we present numerical results of conduction in a disordered quasi-1D wire in the possible presence of magnetic impurities. Our analysis leads us to the study of universal properties in different conduction regimes such as the localized and metallic ones. In particular, we analyse the cross-over between universality classes occurring when the strength of magnetic disorder is increased. For this purpose, we use a numerical Landauer approach, and derive the scattering matrix of the wire from electron's Green's function.Comment: Final version, accepted for publication in New Journ. of Physics, 27 pages, 28 figures. Replaces the earlier shorter preprint arXiv:0910.427

Some algebraic properties of differential operators

First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield of pseudodifferential operators over K by the subalgebra of all differential operators. Second, we show that the Dieudonne' determinant of a matrix pseudodifferential operator with coefficients in a differential subring A of K lies in the integral closure of A in K, and we give an example of a 2x2 matrix differential operator with coefficients in A whose Dieudonne' determiant does not lie in A.Comment: 15 page