Large deviations for non-uniformly expanding maps

We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space average with respect to a physical measure and compare this with the time averages along orbits of the map, showing that the Lebesgue measure of the set of points whose time averages stay away from the space average decays to zero exponentially fast with the number of iterates involved. As easy by-products we deduce escape rates from subsets of the basins of physical measures for these types of maps. The rates of decay are naturally related to the metric entropy and pressure function of the system with respect to a family of equilibrium states. The corrections added to the published version of this text appear in bold; see last section for a list of changesComment: 36 pages, 1 figure. After many PhD students and colleagues having pointed several errors in the statements and proofs, this is a correction to published article answering those comments. List of main changes in a new last sectio

Dilaton Gravity with a Non-minmally Coupled Scalar Field

We discuss the two-dimensional dilaton gravity with a scalar field as the source matter. The coupling between the gravity and the scalar, massless, field is presented in an unusual form. We work out two examples of these couplings and solutions with black-hole behaviour are discussed and compared with those found in the literature

Conformal transformation in bowtie nanoantennas and nanocavities: unveiling hidden symmetries

In this work, bowtie nanoantennas and nanocavities are analyzed using the conformal transformation technique. Their performance is studied in terms of the non-radiative Purcell enhancement and self-induced optical forces experienced by quantum emitters. It is demonstrated how these two geometrically different plasmonic nanoparticles can share the same non-radiative Purcell spectra. This hidden symmetric response is unveiled by properly applying the conformal transformation technique, demonstrating that both nanoparticles share the same transformed geometry

Impact of plasmonic bowtie nanoantennas and nanocavities on the dynamics of nearby nanoemitters

Metallic nanoparticles exert a strong influence on the electrodynamics and mechanical dynamics of nanoemitters in their vicinity. Transformation optics can provide analytical descriptions and physical insight on these scenarios. As a case of study, we discuss the use of conformal transformation to understand the nonradiative Purcell enhancement and the optical forces experienced by nanoemitters nearby bowtie nanocavities and nanoantennas