On the stability of field-theoretical regularizations of negative tension branes

Any attempt to regularize a negative tension brane through a bulk scalar requires that this field is a ghost. One can try to improve in this aspect in a number of ways. For instance, it has been suggested to employ a field whose kinetic term is not sign definite, in the hope that the background may be overall stable. We show that this is not the case; the physical perturbations (gravity included) of the system do not extend across the zeros of the kinetic term; hence, all the modes are entirely localized either where the kinetic term is positive, or where it is negative; this second type of modes are ghosts. We show that this conclusion does not depend on the specific choice for the kinetic and potential functions for the bulk scalar.Comment: 7 pages, 3 figure

Selective excitation of plasmons superlocalized at sharp perturbations of metal nanoparticles

Sharp metal corners and tips support plasmons localized on the scale of the curvature radius -- superlocalized plasmons. We analyze plasmonic properties of nanoparticles with small and sharp corner- and tip-shaped surface perturbations in terms of hybridization of the superlocalized plasmons, which frequencies are determined by the perturbations shape, and the ordinary plasmons localized on the whole particle. When the frequency of a superlocalized plasmon gets close to that of the ordinary plasmon, their strong hybridization occurs and facilitates excitation of an optical hot-spot near the corresponding perturbation apex. The particle is then employed as a nano-antenna that selectively couples the free-space light to the nanoscale vicinity of the apex providing precise local light enhancement by several orders of magnitude

Population Dynamics and Non-Hermitian Localization

We review localization with non-Hermitian time evolution as applied to simple models of population biology with spatially varying growth profiles and convection. Convection leads to a constant imaginary vector potential in the Schroedinger-like operator which appears in linearized growth models. We illustrate the basic ideas by reviewing how convection affects the evolution of a population influenced by a simple square well growth profile. Results from discrete lattice growth models in both one and two dimensions are presented. A set of similarity transformations which lead to exact results for the spectrum and winding numbers of eigenfunctions for random growth rates in one dimension is described in detail. We discuss the influence of boundary conditions, and argue that periodic boundary conditions lead to results which are in fact typical of a broad class of growth problems with convection.Comment: 19 pages, 11 figure

Locality in Network Optimization

In probability theory and statistics notions of correlation among random variables, decay of correlation, and bias-variance trade-off are fundamental. In this work we introduce analogous notions in optimization, and we show their usefulness in a concrete setting. We propose a general notion of correlation among variables in optimization procedures that is based on the sensitivity of optimal points upon (possibly finite) perturbations. We present a canonical instance in network optimization (the min-cost network flow problem) that exhibits locality, i.e., a setting where the correlation decays as a function of the graph-theoretical distance in the network. In the case of warm-start reoptimization, we develop a general approach to localize a given optimization routine in order to exploit locality. We show that the localization mechanism is responsible for introducing a bias in the original algorithm, and that the bias-variance trade-off that emerges can be exploited to minimize the computational complexity required to reach a prescribed level of error accuracy. We provide numerical evidence to support our claims