T-Dualities and Doubled Geometry of the Principal Chiral Model

The Principal Chiral Model (PCM) defined on the group manifold of SU(2) is here investigated with the aim of getting a further deepening of its relation with Generalized and Doubled Geometry. A one-parameter family of equivalent Hamiltonian descriptions is introduced, and cast into the form of Born geometries. Then O(3,3) duality transformations of the target phase space are performed and we show that the resulting dual models are defined on the group SB(2,C) which is the Poisson-Lie dual of SU(2) in the Iwasawa decomposition of the Drinfel'd double SL(2, C). Moreover, starting from the Lagrangian approach, a new kind of duality is found between the SU(2) PCM and the natural one defined on SB(2,C) which is not an isometry of the target phase space. A parent action with doubled degrees of freedom and configuration space SL(2, C) is then defined that reduces to either one of the dually related models, once suitable constraints are implemented.Comment: 41 pages, revised version published in JHE

Metric on the space of quantum states from relative entropy. Tomographic reconstruction

In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a suitably defined coordinate free differential calculus. The cases N = 2, N = 3 are discussed in detail and notable limits are analyzed. The radial limit procedure has been used to recover quantum metrics for lower rank states, such as pure states. By using the tomographic picture of quantum mechanics we have obtained the Fisher- Rao metric for the space of quantum tomograms and derived a reconstruction formula of the quantum metric of density states out of the tomographic one. A new inequality obtained for probabilities of three spin-1/2 projections in three perpendicular directions is proposed to be checked in experiments with superconducting circuits.Comment: 31 pages. No figures. Abstract and Introduction rewritten. Minor corrections. References adde

Jacobi sigma models

We introduce a two-dimensional sigma model on surfaces with boundary and target space a Jacobi manifold. The model yields a topological open string theory. In the Hamiltonian approach first class constraints are derived, which generate gauge invariance of the model under diffeomorphisms. By introducing a metric term, a non-topological sigma model is obtained, yielding a Polyakov action with metric and B-field, whose target space is a Jacobi manifold.Comment: 21 pages. Latex2e. Minor changes, references adde

Doubling, T-Duality and Generalized Geometry: a Simple Model

A simple mechanical system, the three-dimensional isotropic rigid rotator, is here investigated as a 0+1 field theory, aiming at further investigating the relation between Generalized/Double Geometry on the one hand and Doubled World-Sheet Formalism/Double Field Theory, on the other hand. The model is defined over the group manifold of SU(2) and a dual model is introduced having the Poisson-Lie dual of SU(2) as configuration space. A generalized action with configuration space SL(2,C), i.e. the Drinfel'd double of the group SU(2), is then defined: it reduces to the original action of the rotator or to its dual, once constraints are implemented. The new action contains twice as many variables as the original. Moreover, its geometric structures can be understood in terms of Generalized Geometry. keywords: Generalized Geometry, Double Field Theory, T-Duality, Poisson-Lie symmetry.Comment: 37 pages. Revised version to appear in JHE

A Pedagogical Intrinsic Approach to Relative Entropies as Potential Functions of Quantum Metrics: the qq-zz Family

The so-called $q$-z-\textit{R\'enyi Relative Entropies} provide a huge two-parameter family of relative entropies which includes almost all well-known examples of quantum relative entropies for suitable values of the parameters. In this paper we consider a log-regularized version of this family and use it as a family of potential functions to generate covariant $(0,2)$ symmetric tensors on the space of invertible quantum states in finite dimensions. The geometric formalism developed here allows us to obtain the explicit expressions of such tensor fields in terms of a basis of globally defined differential forms on a suitable unfolding space without the need to introduce a specific set of coordinates. To make the reader acquainted with the intrinsic formalism introduced, we first perform the computation for the qubit case, and then, we extend the computation of the metric-like tensors to a generic $n$-level system. By suitably varying the parameters $q$ and $z$, we are able to recover well-known examples of quantum metric tensors that, in our treatment, appear written in terms of globally defined geometrical objects that do not depend on the coordinates system used. In particular, we obtain a coordinate-free expression for the von Neumann-Umegaki metric, for the Bures metric and for the Wigner-Yanase metric in the arbitrary $n$-level case.Comment: 50 pages, 1 figur

Fish assemblage response to environmental pressures in the Venice lagoon

1 - Venice lagoon (Italy), being a transitional water environment, is subjected to several environmental pressures of anthropogenic origin, with a likely impact on the overall ecological status of the system. 2 - Following the Water Framework Directive (WFD, Directive 2000/60/CE), water bodies are to be characterised by the pressures acting on them, and fish assemblages can be used as biological quality element of their ecological status. The Venice lagoon basin has been divided into 14 water bodies, belonging to 5 types, according to the national classification. 3 - With the aim of comparing the role of anthropogenic pressures and environmental background in affecting the lagoon fish assemblages, human pressures have been identified and their magnitude quantified in each lagoon water body, with particular reference to 3 pressure categories: pollution (including nutrient enrichment), direct pressures on the habitat and the living organisms (with particular regard to fishes), and indirect pressures deriving from ground occupation (adjacent land uses). 4 - Fish assemblage attributes (both taxonomical and functional), in sites located within 4 lagoon water bodies (fish samples were collected in 2001-2002 by using fyke nets), were related to the respective pressures acting on these water bodies, by taking into account also the contribution of natural environmental variability among the studied areas, including habitat diversity. 5 - Results showed similar significant effects of environmental background and anthropogenic pressures on the lagoon fish assemblages. This highlights the importance of controlling for environmental variability to allow the detection of the signal of human impact on biological assemblages when attempting at the evaluation of lagoon ecological status. © 2009 University of Salento - SIBA

Using the transparency of supply chain powered by blockchain to improve sustainability relationships with stakeholders in the food sector: The case study of Lavazza

Food product safety and quality are considered to be of the utmost significance on a global scale. Highly publicized food safety incidents have significantly increased public interest in food traceability, defined as “the ability to track any food, feed, food-producing animal or substance that will be used for consumption, through all stages of production, processing, and distribution” (European Union). The World Health Organization (WHO) suggests that governments, producers, and consumers work together to ensure food safety, which calls for the dissemination of pertinent information throughout complex food value networks. Therefore, it is in the best interest of profitdriven businesses to implement information systems for tracking food goods, a significant byproduct of which is the likelihood of increased profitability. This paper aims to explore the ample possibilities for such implementations that are now available thanks to blockchain technology. In particular, the goal is to explore the dynamics of this technology and identify how it helps to create good customer relationships. For this purpose, the case of Lavazza, an important Italian roasted coffee company that has recently introduced a blockchain-tracked product to the market, is analyzed in detail, including all the steps that made the application of the technology possible and how it was finally communicated to the consumer. The case study offers a concrete example that resulted from both stakeholders’ internal need for greater traceability and consumers’ external need for greater transparency regarding the company’s sourcing processes. In this pilot project, collaboration among all the entities that are part of the chain was essential to delivering a formative, customized, and ultimately, easy-to-understand experience to the end consumer. Finally, Lavazza is an example of a company that decided to challenge itself by following a trend that will be increasingly present in future socioeconomic scenarios