Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs

Manifestly non-Hermitian quantum graphs with real spectra are introduced and shown tractable as a new class of phenomenological models with several appealing descriptive properties. For illustrative purposes, just equilateral star-graphs are considered here in detail, with non-Hermiticities introduced by interactions attached to the vertices. The facilitated feasibility of the analysis of their spectra is achieved via their systematic approximative Runge-Kutta-inspired reduction to star-shaped discrete lattices. The resulting bound-state spectra are found real in a discretization-independent interval of couplings. This conclusion is reinterpreted as the existence of a hidden Hermiticity of our models, i.e., as the standard and manifest Hermiticity of the underlying Hamiltonian in one of less usual, {\em ad hoc} representations ${\cal H}_j$ of the Hilbert space of states in which the inner product is local (at $j=0$) or increasingly nonlocal (at $j=1,2, ...$). Explicit examples of these (of course, Hamiltonian-dependent) hermitizing inner products are offered in closed form. In this way each initial quantum graph is assigned a menu of optional, non-equivalent standard probabilistic interpretations exhibiting a controlled, tunable nonlocality.Comment: 33 pp., 6 figure

The prevalence of blinding trachoma in northern states of Sudan.

BACKGROUND: Despite historical evidence of blinding trachoma, there have been no widespread contemporary surveys of trachoma prevalence in the northern states of Sudan. We aimed to conduct district-level surveys in this vast region in order to map the extent of the problem and estimate the need for trachoma control interventions to eliminate blinding trachoma. METHODS AND FINDINGS: Separate, population based cross-sectional surveys were conducted in 88 localities (districts) in 12 northern states of Sudan between 2006 and 2010. Two-stage cluster random sampling with probability proportional to size was used to select the sample. Trachoma grading was done using the WHO simplified grading system. Key prevalence indicators were trachomatous inflammation-follicular (TF) in children aged 1-9 years and trachomatous trichiasis (TT) in adults aged 15 years and above. The sample comprised 1,260 clusters from which 25,624 households were surveyed. A total of 106,697 participants (81.6% response rate) were examined for trachoma signs. TF prevalence was above 10% in three districts and between 5% and 9% in 11 districts. TT prevalence among adults was above 1% in 20 districts (which included the three districts with TF prevalence >10%). The overall number of people with TT in the population was estimated to be 31,072 (lower and upper bounds = 26,125-36,955). CONCLUSION: Trachoma mapping is complete in the northern states of Sudan except for the Darfur States. The survey findings will facilitate programme planning and inform deployment of resources for elimination of trachoma from the northern states of Sudan by 2015, in accordance with the Sudan Federal Ministry of Health (FMOH) objectives

q-breathers in Discrete Nonlinear Schroedinger lattices

$q$-breathers are exact time-periodic solutions of extended nonlinear systems continued from the normal modes of the corresponding linearized system. They are localized in the space of normal modes. The existence of these solutions in a weakly anharmonic atomic chain explained essential features of the Fermi-Pasta-Ulam (FPU) paradox. We study $q$-breathers in one- two- and three-dimensional discrete nonlinear Sch\"{o}dinger (DNLS) lattices -- theoretical playgrounds for light propagation in nonlinear optical waveguide networks, and the dynamics of cold atoms in optical lattices. We prove the existence of these solutions for weak nonlinearity. We find that the localization of $q$-breathers is controlled by a single parameter which depends on the norm density, nonlinearity strength and seed wave vector. At a critical value of that parameter $q$-breathers delocalize via resonances, signaling a breakdown of the normal mode picture and a transition into strong mode-mode interaction regime. In particular this breakdown takes place at one of the edges of the normal mode spectrum, and in a singular way also in the center of that spectrum. A stability analysis of $q$-breathers supplements these findings. For three-dimensional lattices, we find $q$-breather vortices, which violate time reversal symmetry and generate a vortex ring flow of energy in normal mode space.Comment: 19 pages, 9 figure

Numerical and Experimental Study of Natural Convection Air Flow in a Solar Tower Dryer

This work focuses on the study of the flow of air in natural convection in a solar tower of small size. The behavior of air in the tower, considered as a solar dryer, provides information on the amount of heat absorbed by the air upon entry into the collector. A theoretical approach allows us to theoretically simulate the flow by using a mathematical model characterizing the physical parameters of the system during a daily sunshine. An analysis of this phenomenon is made and results are obtained

Optical and Thermal Performance Analysis of a Steady Spherical Collector with a Crescent-shaped Rotating Absorber

In this paper, optical analysis of spherical concentrator is made to determine the local and the global geometric concentration, as knowing the geometric concentration of a system can help predict what temperatures can possibly be obtained with it.This leads to conclude that spherical collectors may produce higher temperatures than parabolic trough, and they could even be sharply improved by using a mixt cylindrical and cavity (or flat) absorber. A craft prototype of a steady spherical concentrator made with concreteand having a smooth inner surface mapped with mirror tape is presented. Its absorber is made with blacken steel sheets and shaped like a moon crescent to be aligned with the declination plan and to avoid motorization for the tracking of the sun from East to West. Experimental measurements lead to temperatures reaching 686°C on the curve of the least diffusion, and 252°C in the absorber oven-like reservoir. Overall, the resultsuggests higher potentialities of spherical collectors,which also show possibility of use with much reduced tracking system and less vulnerability to bad weather

PT-symmetric deformations of Calogero models

We demonstrate that Coxeter groups allow for complex PT-symmetric deformations across the boundaries of all Weyl chambers. We compute the explicit deformations for the A2 and G2-Coxeter group and apply these constructions to Calogero–Moser–Sutherland models invariant under the extended Coxeter groups. The eigenspectra for the deformed models are real and contain the spectra of the undeformed case as subsystems

Quantum inner-product metrics via recurrent solution of Dieudonne equation

A given Hamiltonian matrix H with real spectrum is assumed tridiagonal and non-Hermitian. Its possible Hermitizations via an amended, ad hoc inner-product metric are studied. Under certain reasonable assumptions, all of these metrics are shown obtainable as recurrent solutions of the hidden Hermiticity constraint called Dieudonne equation. In this framework even the two-parametric Jacobi-polynomial real- and asymmetric-matrix N-site lattice Hamiltonian is found tractable non-numerically at all N.Comment: 21 p

Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators

Parallels between the notions of nonlinear pseudobosons and of an apparent non-Hermiticity of observables as shown in paper I (arXiv: 1109.0605) are demonstrated to survive the transition to the quantum models based on the use of unbounded metric in the Hilbert space of states.Comment: 21 p