Reconfigurable photonic integrated mode (de)multiplexer for SDM fiber transmission

A photonic integrated circuit for mode multiplexing and demultiplexing in a few-mode fiber is presented and demonstrated. Two 10 Gbit/s channels at the same wavelength and polarization are simultaneously transmitted over modes LP01 and LP11a of a few-mode fiber exploiting the integrated mode MUX and DEMUX. The proposed Indium-Phosphide-based circuits have a good coupling efficiency with fiber modes with mode-dependant loss smaller than 1 dB. Measured mode excitation cross-talk is as low as -20 dB and a channel cross-talk after propagation and demultiplexing of -15 dB is achieved. An operational bandwidth of the full transmission system of at least 10 nm is demonstrated. Both mode MUX and DEMUX are fully reconfigurable and allow a dynamic switch of channel routing in the transmission system

The MINI mixed finite element for the Stokes problem: An experimental investigation

Super-convergence of order 1.5 in pressure and velocity has been experimentally investigated for the two-dimensional Stokes problem discretised with the MINI mixed finite element. Even though the classic mixed finite element theory for the MINI element guarantees linear convergence for the total error, recent theoretical results indicate that super-convergence of order 1.5 in pressure and of the linear part of the computed velocity to the piecewise linear nodal interpolation of the exact velocity is in fact possible with structured, three-directional triangular meshes. The numerical experiments presented here suggest a more general validity of super-convergence of order 1.5, possibly to automatically generated and unstructured triangulations. In addition, the approximating properties of the complete computed velocity have been compared with the approximating properties of the piecewise-linear part of the computed velocity, finding that the former is generally closer to the exact velocity, whereas the latter conserves mass better

Social Aggregation as a Cooperative Game

A new approach for the description of phenomena of social aggregation is suggested. On the basis of psychological concepts (as for instance social norms and cultural coordinates), we deduce a general mechanism for the social aggregation in which different clusters of individuals can merge according to the cooperation among the agents. In their turn, the agents can cooperate or defect according to the clusters distribution inside the system. The fitness of an individual increases with the size of its cluster, but decreases with the work the individual had to do in order to join it. In order to test the reliability of such new approach, we introduce a couple of simple toy models with the features illustrated above. We see, from this preliminary study, how the cooperation is the most convenient strategy only in presence of very large clusters, while on the other hand it is not necessary to have one hundred percent of cooperators for reaching a totally ordered configuration with only one megacluster filling the whole system.Comment: 18 pages, 10 figure

Off-shell renormalization in the presence of dimension 6 derivative operators. II. UV coefficients

The full off-shell one loop renormalization for all divergent amplitudes up to dimension 6 in the Abelian Higgs-Kibble model, supplemented with a maximally power counting violating higher-dimensional gauge-invariant derivative interaction $\sim g ~ \phi^\dagger \phi (D^\mu \phi)^\dagger D_\mu \phi$, is presented. This allows one to perform the complete renormalization of radiatively generated dimension 6 operators in the model at hand. We describe in details the technical tools required in order to disentangle the contribution to UV divergences parameterized by (generalized) non-polynomial field redefinitions. We also discuss how to extract the dependence of the $\beta$-function coefficients on the non-renormalizable coupling $g$ in one loop approximation, as well as the cohomological techniques (contractible pairs) required to efficiently separate the mixing of contributions associated to different higher-dimensional operators in a spontaneously broken effective field theory.Comment: 33 pages; revised version including the derivation of the one-loop beta function

Polya-Szego inequality and Dirichlet pp-spectral gap for non-smooth spaces with Ricci curvature bounded below

We study decreasing rearrangements of functions defined on (possibly non-smooth) metric measure spaces with Ricci curvature bounded below by $K>0$ and dimension bounded above by $N\in (1,\infty)$ in a synthetic sense, the so called $CD(K,N)$ spaces. We first establish a Polya-Szego type inequality stating that the $W^{1,p}$-Sobolev norm decreases under such a rearrangement and apply the result to show sharp spectral gap for the $p$-Laplace operator with Dirichlet boundary conditions (on open subsets), for every $p\in (1,\infty)$. This extends to the non-smooth setting a classical result of B\'erard-Meyer and Matei; remarkable examples of spaces fitting out framework and for which the results seem new include: measured-Gromov Hausdorff limits of Riemannian manifolds with Ricci$\geq K>0$, finite dimensional Alexandrov spaces with curvature$\geq K>0$, Finsler manifolds with Ricci$\geq K>0$. In the second part of the paper we prove new rigidity and almost rigidity results attached to the aforementioned inequalities, in the framework of $RCD(K,N)$ spaces, which seem original even for smooth Riemannian manifolds with Ricci$\geq K>0$.Comment: 33 pages. Final version published in Journal de Math\'ematiques Pures et Appliqu\'ee

Off-shell renormalization in the presence of dimension 6 derivative operators. I. General theory

The consistent recursive subtraction of UV divergences order by order in the loop expansion for spontaneously broken effective field theories with dimension-6 derivative operators is presented for an Abelian gauge group. We solve the Slavnov-Taylor identity to all orders in the loop expansion by homotopy techniques and a suitable choice of invariant field coordinates (named bleached variables) for the linearly realized gauge group. This allows one to disentangle the gauge-invariant contributions to off-shell 1-PI amplitudes from those associated with the gauge-fixing and (generalized) non-polynomial field redefinitions (that do appear already at one loop). The tools presented can be easily generalized to the non-Abelian case.Comment: 37 pages, 3 figures; updated version to match the published on

Off-shell renormalization in Higgs effective field theories

The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential $\sim\left(\Phi^\dagger\Phi-\frac{v^2}2\right)^N$ with $N$ arbitrary is presented. This is achieved by renormalizing the theory once reformulated in terms of two auxiliary fields $X_{1,2}$, which, due to the invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly constrained by functional identities. The latter allow in turn the explicit derivation of the mapping onto the original theory, through which the (divergent) multi-Higgs amplitude are generated in a purely algebraic fashion. We show that, contrary to naive expectations based on the loss of power counting renormalizability, the Higgs field undergoes a linear Standard Model like redefinition, and evaluate the renormalization of the complete set of Higgs self-coupling in the $N\to\infty$ case.Comment: 33 pages, no figures. v3: complete one-loop off-shell renormalization for a BSM potential involving arbitrary powers of $\left(\phi^\dagger\phi-\frac{v^2}2\right)$ presented; Higgs wavefunction renormalization shown to be SM like; renormalization of the complete set of Higgs self-coupling in the $N\to\infty$ case discussed. v3 matches the published on

Canonical transformations in gauge theories with non-trivial backgrounds

We show how to implement the background field method by means of canonical transformations and comment on the applications of the method to non-perturbative techniques in non-Abelian gauge theories. We discuss the case of the lattice in some details.Comment: 6 pages. Prepared for the Sixth International Conference on Quarks and Nuclear Physics QNP2012, April 16-20, 2012, Ecole Polytechnique, Palaiseau, Pari

Magneto-transport from momentum dissipating holography

We obtain explicit expressions for the thermoelectric transport coefficients of a strongly coupled, planar medium in the presence of an orthogonal magnetic field and momentum-dissipating processes. The computations are performed within the gauge/gravity framework where the momentum dissipation mechanism is introduced by including a mass term for the bulk graviton. Relying on the structure of the computed transport coefficients and promoting the parameters to become dynamical functions, we propose a holography inspired phenomenology open to a direct comparison with experimental data from the cuprates.Comment: 23 page

Send in the clowns. Humor and power in Italian political, social and cultural life

No abstract available