Distributional approach to point interactions in one-dimensional quantum mechanics

We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the Schr\"odinger and Dirac equations is replaced by a well-defined distribution satisfying some simple mathematical conditions and, in addition, the physical requirement of probability current conservation is imposed. A four-parameter family of interactions thus emerges as the most general point interaction both in the non-relativistic and in the relativistic theories (in agreement with results obtained by self-adjoint extensions). Since the interaction is given explicitly, the distributional method allows one to carry out symmetry investigations in a simple way, and it proves to be useful to clarify some ambiguities related to the so-called $\delta^\prime$ interaction.Comment: Open Access link: http://journal.frontiersin.org/Journal/10.3389/fphy.2014.00023/abstrac

HodgeRank as a new tool to explore the structure of a social representation

Social representation theory is a branch of social psychology that aims to identify the framework of concepts, ideas, opinions, beliefs, or feelings shared by the individuals within a social group, regarding a social object. Two main problems arise in this theory. The first concerns the identification of the content of the representation, which is the set of cognitive elements shared by the group; the second concerns its structure, which is the way these elements are organized and related among themselves. It is desirable that the methods to address these problems be simple, in regards to the feasibility of the data collection, and reliable, in the sense that they should provide a clear picture of the content and the structure of the representation. No single method proposed in the literature until now fully satisfies these features at the same time. Here we propose the use of HodgeRank, a global ranking method based on the Hodge combinatorial theory, as a new tool to explore the structure of a social representation. In this proposal, the input data is the same as those required for the hierarchical word associations, which is the main method in the field of social representations. However, the HodgeRank provides richer results when compared to the usual approach to analysing this kind of data, based on the Vergés’ double-entry table. The main outcome of the HodgeRank is a graph, analogous to an electric circuit, from which some structural elements of the representation can already be identified. Moreover, the HodgeRank technique identifies the sources of inconsistencies between the global ranking and the aggregated answers within the social group. We interpret such inconsistencies in terms of the stability of the representation and use them to raise conjectures about the potential dynamics of the representation. We illustrate the application of this method in the study of a social representation of COVID-19 within a group of students and also within a group of faculty members from higher education institutions in Brazil

On the Salecker-Wigner-Peres clock and double barrier tunneling

In this work we revisit the Salecker-Wigner-Peres clock formalism and show that it can be directly applied to the phenomenon of tunneling. Then we apply this formalism to the determination of the tunneling time of a non relativistic wavepacket, sharply concentrated around a tunneling energy, incident on a symmetric double barrier potential. In order to deepen the discussion about the generalized Hartmann effect, we consider the case in which the clock runs only when the particle can be found inside the region \emph{between} the barriers and show that, whenever the probability to find the particle in this region is non negligible, the corresponding time (which in this case turns out to be a dwell time) increases with the barrier spacing.Comment: To appear in Phys. Rev.

Topological phases from higher gauge symmetry in 3+1 dimensions

We propose an exactly solvable Hamiltonian for topological phases in 3 + 1 dimensions utilizing ideas from higher lattice gauge theory, where the gauge symmetry is given by a finite 2-group. We explicitly show that the model is a Hamiltonian realization of Yetter's homotopy 2-type topological quantum field theory whereby the ground-state projector of the model defined on the manifold M 3 is given by the partition function of the underlying topological quantum field theory for M 3 × [ 0 , 1 ] . We show that this result holds in any dimension and illustrate it by computing the ground state degeneracy for a selection of spatial manifolds and 2-groups. As an application we show that a subset of our model is dual to a class of Abelian Walker-Wang models describing 3 + 1 dimensional topological insulators

Development of an ultraviolet-c irradiation room in a public Portuguese hospital for safe re-utilization of personal protective respirators

Almost two years have passed since COVID-19 was officially declared a pandemic by the World Health Organization. However, it still holds a tight grasp on the entire human population. Several variants of concern, one after another, have spread throughout the world. The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) omicron variant may become the fastest spreading virus in history. Therefore, it is more than evident that the use of personal protective equipment (PPE) will continue to play a pivotal role during the current pandemic. This work depicts an integrative approach attesting to the effectiveness of ultra-violet-C (UV-C) energy density for the sterilization of personal protective equipment, in particular FFP2 respirators used by the health care staff in intensive care units. It is increasingly clear that this approach should not be limited to health care units. Due to the record-breaking spreading rates of SARS-CoV-2, it is apparent that the use of PPE, in particular masks and respirators, will remain a critical tool to mitigate future pandemics. Therefore, similar UV-C disinfecting rooms should be considered for use within institutions and companies and even incorporated within household devices to avoid PPE shortages and, most importantly, to reduce environmental burdens.This research was funded by the Portuguese Foundation for Science and Technology (FCT), European Regional Development Fund (FEDER), Operational Program for Competitive ness Factors (COMPETE), and Portuguese Ministry of Science, Technology and Higher Education (MCTS) [UID/CTM/00264/2021]; [PTDC/CTM TEX/28295/2017]; [PTDC/CTM-TEX/1213/2020]; [UIDB/50026/2020]; [NORTE-01-0145-FEDER-072555]; [NORTE-01-0145-FEDER-000039] and con tract funding [2020.03113.CEECIND] to M.I.V. This work is a result of a project with the EXMA company in co-promotion with the University of Minho [NORTE-01-02B7-FEDER-048968] and supported by the Northern Portugal Regional Operational Program (NORTE 2020) under the PORTUGAL 2020 Partnership Agreement through the FEDER. Finally, this project was funded by the FCT Research4COVID-19 special fund [011_595803006UV-Fast]

A protocol update for the Selenium Treatment and Chagasic Cardiomyopathy (STCC) trial

Abstract Several studies evaluating clinical forms of chronic Chagas disease show that about one-third of patients present cardiac involvement. Heart failure, sudden death and cardioembolic stroke are the main mechanisms of death in Chagas heart disease. The impact of specific etiologic treatment on the prognosis of patients with chronic Chagas heart disease is very limited regardless of the presence or absence of heart failure. Patients with symptomatic Chagas heart disease present serum selenium (Se) levels lower than patients without Chagas heart disease. Moreover, Se supplementation in animal models showed promising results. The aim of this trial is to estimate the effect of Se treatment on prevention of heart disease progression in patients with Chagas cardiomyopathy. However, we had to introduce some protocol modifications in order to keep trial feasibility, as follows: the primary outcome was restricted to left ventricular ejection fraction as a continuous variable, excluding disease progression; the follow-up period was decreased from 5 years to 1 year, an adjustment that might increase the participation rate of our study; the superior age limit was increased from 65 to 75 years; and diabetes mellitus was no longer considered an exclusion criterion. All of these protocol modifications were extensively debated by the research team enrolled in the design, recruitment and conduction of the clinical trial to guarantee a high scientific quality. Trial registration Clinical Trials.gov, NCT00875173. Registered on 20 October 2008