N=2 Chern-Simons-Matter Theories Without Vortices

We study ${\cal N}=2$ Chern-Simons-matter theories with gauge group $U_{k_1}(1)\times U_{k_2}(1)$. We find that, when $k_1+k_2=0$, the partition function computed by localization dramatically simplifies and collapses to a single term. We show that the same condition prevents the theory from having supersymmetric vortex configurations. The theories include mass-deformed ABJM theory with $U(1)_{k}\times U_{-k}(1)$ gauge group as a particular case. Similar features are shared by a class of CS-matter theories with gauge group $U_{k_1}(1)\times \cdots \times U_{k_N}(1)$.Comment: 17 page

Double-gated graphene-based devices

We discuss transport through double gated single and few layer graphene devices. This kind of device configuration has been used to investigate the modulation of the energy band structure through the application of an external perpendicular electric field, a unique property of few layer graphene systems. Here we discuss technological details that are important for the fabrication of top gated structures, based on electron-gun evaporation of SiO$_2$. We perform a statistical study that demonstrates how --contrary to expectations-- the breakdown field of electron-gun evaporated thin SiO$_2$ films is comparable to that of thermally grown oxide layers. We find that a high breakdown field can be achieved in evaporated SiO$_2$ only if the oxide deposition is directly followed by the metallization of the top electrodes, without exposure to air of the SiO$_2$ layer.Comment: Replaced with revised version. To appear on New Journal of Physic

Lowest order Virtual Element approximation of magnetostatic problems

We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general decompositions of the computational domain (as is natural for Virtual Element Methods) and uses as unknowns the (constant) tangential component of the magnetic field $\mathbf{H}$ on each edge, and the vertex values of the Lagrange multiplier $p$ (used to enforce the solenoidality of the magnetic induction $\mathbf{B}=\mu\mathbf{H}$). In this respect the method can be seen as the natural generalization of the lowest order Edge Finite Element Method (the so-called "first kind N\'ed\'elec" elements) to polyhedra of almost arbitrary shape, and as we show on some numerical examples it exhibits very good accuracy (for being a lowest order element) and excellent robustness with respect to distortions

Bias-dependent Contact Resistance in Rubrene Single-Crystal Field-Effect Transistors

We report a systematic study of the bias-dependent contact resistance in rubrene single-crystal field-effect transistors with Ni, Co, Cu, Au, and Pt electrodes. We show that the reproducibility in the values of contact resistance strongly depends on the metal, ranging from a factor of two for Ni to more than three orders of magnitude for Au. Surprisingly, FETs with Ni, Co, and Cu contacts exhibits an unexpected reproducibility of the bias-dependent differential conductance of the contacts, once this has been normalized to the value measured at zero bias. This reproducibility may enable the study of microscopic carrier injection processes into organic semiconductors.Comment: 4 pages, 4 figure

Real decoupling ghost quantization of the CGHS model for two dimensional black holes

A complete RST quantization of a CGHS model plus Strominger term is carried out. In so doing a conformal invariant theory with $\kappa=\frac{N}{12}$ is found, that is, without ghosts contribution. The physical consequences of the model are analysed and positive definite Hawking radiation is found.Comment: 14 pages, latex, no figures, marginal errors correcte

Serendipity Face and Edge VEM Spaces

We extend the basic idea of Serendipity Virtual Elements from the previous case (by the same authors) of nodal ($H^1$-conforming) elements, to a more general framework. Then we apply the general strategy to the case of $H(div)$ and $H(curl)$ conforming Virtual Element Methods, in two and three dimensions

Bounds for the relative n-th nilpotency degree in compact groups

The line of investigation of the present paper goes back to a classical work of W. H. Gustafson of the 1973, in which it is described the probability that two randomly chosen group elements commute. In the same work, he gave some bounds for this kind of probability, providing information on the group structure. We have recently obtained some generalizations of his results for finite groups. Here we improve them in the context of the compact groups.Comment: 9 pages; to appear in Asian-European Journal of Mathematics with several improvement