The critical transition of Coulomb impurities in gapped graphene

The effect of supercritical charge impurities in graphene is very similar to the supercritical atomic collapses in QED for Z > 137, but with a much lower critical charge. In this sense graphene can be considered as a natural testing ground for the analysis of quantum field theory vacuum instabilities. We analyze the quantum transition from subcritical to supercritical charge regimes in gapped graphene in a common framework that preserves unitarity for any value of charge impurities. In the supercritical regime it is possible to introduce boundary conditions which control the singular behavior at the impurity. We show that for subcritical charges there are also non-trivial boundary conditions which are similar to those that appear in QED for nuclei in the intermediate regime 118<Z<137. We analyze the behavior of the energy levels associated to the different boundary conditions. In particular, we point out the existence of new bound states in the subcritical regime which include a negative energy bound state in the attractive Coulomb regime. A remarkable property is the continuity of the energy spectral flow under variation of the impurity charge even when jumping across the critical charge transition. We also remark that the energy levels of Hydrogenoid bound states at critical values of charge impurities act as focal points of the spectral flow.Comment: 24 pages, 7 figure

Cultural districts and economic development

The aim of this paper is to analyze the economic properties as well as tbe institutions governing the start-up and the evolution of cultural districts. Cultural districts are a good example of economic development based on localized culture. The first part of the paper (sections 1-3) reviews the relationships between culture, viewed as an idiosyncratic good, and the theory of industrial districts. The sections 4-6 of the paper present a discussion of two models of cultural districts: the industrial cultural district (mainly based on positive externalities, localized culture, and traditions in "arts and crafts"), and the institutional cultural district (mainly based on property rights assigmnent and symbolic values). The section 7 deals with other models of quasi-industrial-districts, namely the museum cultural district (mainly based on network externalities and the search for optimal size), and the metropolitan cultural district (mainly based on communication technology,performing arts, leisure time industries and e-commerce). Policy issues will be analyzed in the final section 8. The hypothesis of a possible convergence of all districts models towards the institutional district, based on the creation of a system of property rights as a means to protect localized production will be discussed.

Workplace Bullying in Italy. Malicious Intent and Role of Anti-discrimination Law. WP C.S.D.L.E. “Massimo D’Antona”.IT – 399/2019

Over the last two decades of the 20th century, bullying in the workplace has been the subject of much attention from Italian labour lawyers and courts. The paper provides an analysis and critique of judicial approaches to defining workplace bullying. It focuses on the two main critical aspects relating to the judge-made de?nition, in particular the role played by the malicious intent of the perpetrator of harassment, on the one hand, and that of other typical elements of the notion of bullying developed in case law and by legal scholars, i.e. continuity between the single events. It is argued that, after some significant developments of case law, the concept of bullying in the workplace appears closer to that of harassment/discrimination under EU and Italian legislation, with the practical implication that most sophisticated anti-discrimination protection techniques aimed at countering harassment by employers could be applicable to various kinds of mobbing. This study also considers the dichotomous approach recently adopted by the Italian Court of Cassation, which has also gone far beyond the notion of mobbing in the strict sense and introduced a new and distinct legal category in order to bring the hitherto excluded cases of harassment back into the scope of protection

Market Piracy in the Design-Based Industry : Economics and Policy regulation

Market piracy in the design-based industry is an expanding worldwide phenomenon (Grossman and Shapiro, 1988a,b; Chaudhry and Walsh, 1996; Schultz II and Saprito, 1996). It deserves a great deal of attention both because of its impressive international dimension (Verma, 1996) and its intrinsic illegality, ambiguity and powerfull potential links with criminal organizations (Andreano and Sigfried, 1980; Fiorentini and Peltzman, 1995). The aim of this paper is to develop theoretical arguments about economic agents' behavior and to shed some light on the main regulatory issues of illegal markets. At a first sight the room for rational incentives to commercial piracy is self-evident. On one hand, an original backpack by the Italian stylist Prada costs, for instance, $510 in Manhattan, New York, and a bootleg copy costs$ 70 in Rome, just in front of Castel Sant'Angelo. On the other hand, the number of units sold can be impressive: as an example Louis Vuitton sells 3.5 millions units per year. Market piracy is usually noticed in sectors such as luxury goods or fashion, but piracy can also be observed in more traditional sectors such as car manufacturers, "bureautic" industry, cooking utensils, aircraft-parts and so on.

Deformation Behavior of Clay-Water Suspensions

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