Interpolation of bilinear operators and compactness

The behavior of bilinear operators acting on interpolation of Banach spaces for the $\rho$ method in relation to the compactness is analyzed. Similar results of Lions-Peetre, Hayakawa and Person's compactness theorems are obtained for the bilinear case and the $\rho$ method.Comment: This work was published at "Nonlinear Analysis: Theory, Methods and Applications, Volume 73, Issue 2, 2010, Pages 526-537". Since there are some gaps in the original proof of Theorem 4.3, Here we give a new proof. For this, we change the Lemma 4.

Comprehensive study of the critical behavior in the diluted antiferromagnet in a field

We study the critical behavior of the Diluted Antiferromagnet in a Field with the Tethered Monte Carlo formalism. We compute the critical exponents (including the elusive hyperscaling violations exponent $\theta$). Our results provide a comprehensive description of the phase transition and clarify the inconsistencies between previous experimental and theoretical work. To do so, our method addresses the usual problems of numerical work (large tunneling barriers and self-averaging violations).Comment: 4 pages, 2 figure

Temperature chaos is a non-local effect

Temperature chaos plays a role in important effects, like for example memory and rejuvenation, in spin glasses, colloids, polymers. We numerically investigate temperature chaos in spin glasses, exploiting its recent characterization as a rare-event driven phenomenon. The peculiarities of the transformation from periodic to anti-periodic boundary conditions in spin glasses allow us to conclude that temperature chaos is non-local: no bounded region of the system causes it. We precise the statistical relationship between temperature chaos and the free-energy changes upon varying boundary conditions.Comment: 15 pages, 8 figures. Version accepted for publication in JSTA

The Coulomb-Higgs transition of the three-parameter U(1)-Higgs model

We find a first order Coulomb--Higgs phase transition at moderately large values of the coupling $\lambda$, and no evidence for a change of order at any finite value of it.Comment: 3 pages, uuencoded compressed ps file. Contribution to Lattice '9

Real space mapping of topological invariants using artificial neural networks

Topological invariants allow to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wavefunctions under twisted boundary conditions. However, those procedures do not allow to calculate a topological invariant by evaluating the system locally, and thus require information about the wavefunctions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a 1-D topological superconductor and a 2-D quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the Kernel Polynomial Method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.Comment: 9 pages, 6 figure

Turning waves and breakdown for incompressible flows

We consider the evolution of an interface generated between two immiscible incompressible and irrotational fluids. Specifically we study the Muskat and water wave problems. We show that starting with a family of initial data given by (\al,f_0(\al)), the interface reaches a regime in finite time in which is no longer a graph. Therefore there exists a time $t^*$ where the solution of the free boundary problem parameterized as (\al,f(\al,t)) blows-up: \|\da f\|_{L^\infty}(t^*)=\infty. In particular, for the Muskat problem, this result allows us to reach an unstable regime, for which the Rayleigh-Taylor condition changes sign and the solution breaks down.Comment: 15 page

The Cosmic Near Infrared Background: Remnant Light from Early Stars

The redshifted ultraviolet light from early stars at z ~ 10 contributes to the cosmic near infrared background. We present detailed calculations of its spectrum with various assumptions about metallicity and mass spectrum of early stars. We show that if the near infrared background has a stellar origin, metal-free stars are not the only explanation of the excess near infrared background; stars with metals (e.g. Z=1/50 Z_sun) can produce the same amount of background intensity as the metal-free stars. We quantitatively show that the predicted average intensity at 1-2 microns is essentially determined by the efficiency of nuclear burning in stars, which is not very sensitive to metallicity. We predict \nu I_\nu / \dot{\rho}_* ~ 4-8 nW m^-2 sr^-1, where \dot{\rho_*} is the mean star formation rate at z=7-15 (in units of M_sun yr^-1 Mpc^-3) for stars more massive than 5 M_sun. On the other hand, since we have very little knowledge about the form of mass spectrum of early stars, uncertainty in the average intensity due to the mass spectrum could be large. An accurate determination of the near infrared background allows us to probe formation history of early stars, which is difficult to constrain by other means. While the star formation rate at z=7-15 inferred from the current data is significantly higher than the local rate at z<5, it does not rule out the stellar origin of the cosmic near infrared background. In addition, we show that a reasonable initial mass function, coupled with this star formation rate, does not over-produce metals in the universe in most cases, and may produce as little as less than 1 % of the metals observed in the universe today.Comment: 37 pages, 7 figures, (v2) Changes to abstract to emphasize that the excess near infrared background can solely be explained by stars with significant metals. (Metal-free stars are not necessarily needed.) (v3) Expanded discussion on the metallicity constraint. Accepted for publication in Ap