Abelian Hall Fluids and Edge States: a Conformal Field Theory Approach

We show that a Coulomb gas Vertex Operator representation of 2D Conformal Field Theory gives a complete description of abelian Hall fluids: as an euclidean theory in two space dimensions leads to the construction of the ground state wave function for planar and toroidal geometry and characterizes the spectrum of low energy excitations; as a $1+1$ Minkowski theory gives the corresponding dynamics of the edge states. The difference between a generic Hall fluid and states of the Jain's sequences is emphasized and the presence, in the latter case, of of an $\hat {U}(1)\otimes \hat {SU}(n)$ extended algebra and the consequent propagation on the edges of a single charged mode and $n-1$ neutral modes is discussed.Comment: Latex, 22 page

Knizhnik-Zamolodchikov equation and extended symmetry for stable Hall states

We describe a $n$ component abelian Hall fluid as a system of {\it composite bosons} moving in an average null field given by the external magnetic field and by the statistical flux tubes located at the position of the particles. The collective vacuum state, in which the bosons condense, is characterized by a Knizhnik-Zamolodchikov differential equation relative to a $\hat {U}(1)^n$ Wess-Zumino model. In the case of states belonging to Jain's sequences the Knizhnik-Zamolodchikov equation naturally leads to the presence of an \hat{U}(1)\ot \hat{SU}(n) extended algebra. Only the $\hat{U}(1)$ mode is charged while the $\hat{SU}(n)$ modes are neutral, in agreement with recent results obtained in the study of the edge states.Comment: 11 pages, Late

2+1 Einstein Gravity as a Deformed Chern-Simons Theory

The usual description of 2+1 dimensional Einstein gravity as a Chern-Simons (CS) theory is extended to a one parameter family of descriptions of 2+1 Einstein gravity. This is done by replacing the Poincare' gauge group symmetry by a q-deformed Poincare' gauge group symmetry, with the former recovered when q-> 1. As a result, we obtain a one parameter family of Hamiltonian formulations for 2+1 gravity. Although formulated in terms of noncommuting dreibeins and spin-connection fields, our expression for the action and our field equations, appropriately ordered, are identical in form to the ordinary ones. Moreover, starting with a properly defined metric tensor, the usual metric theory can be built; the Christoffel symbols and space-time curvature having the usual expressions in terms of the metric tensor, and being represented by c-numbers. In this article, we also couple the theory to particle sources, and find that these sources carry exotic angular momentum. Finally, problems related to the introduction of a cosmological constant are discussed.Comment: Latex file, 26 pages, no figure

Comments on the Non-Commutative Description of Classical Gravity

We find a one-parameter family of Lagrangian descriptions for classical general relativity in terms of tetrads which are not c-numbers. Rather, they obey exotic commutation relations. These noncommutative properties drop out in the metric sector of the theory, where the Christoffel symbols and the Riemann tensor are ordinary commuting objects and they are given by the usual expression in terms of the metric tensor. Although the metric tensor is not a c-number, we argue that all measurements one can make in this theory are associated with c-numbers, and thus that the common invariant sector of our one--parameter family of deformed gauge theories (for the case of zero torsion) is physically equivalent to Einstein's general relativity.Comment: Latex file, 13 pages, no figure

Comment on "Quantitative wave-particle duality in multibeam interferometers"

In a recent paper [Phys. Rev. {\bf A64}, 042113 (2001)] S. D\"urr proposed an interesting multibeam generalization of the quantitative formulation of interferometric wave-particle duality, discovered by Englert for two-beam interferometers. The proposed generalization is an inequality that relates a generalized measure of the fringe visibility, to certain measures of the maximum amount of which-way knowledge that can be stored in a which-way detector. We construct an explicit example where, with three beams in a pure state, the scheme proposed by D\"{u}rr leads to the possibility of an ideal which-way detector, that can achieve a better path-discrimination, at the same time as a better fringe visibility. In our opinion, this seems to be in contrast with the intuitive idea of complementarity, as it is implemented in the two-beams case, where an increase in path discrimination always implies a decrease of fringe visibility, if the beams and the detector are in pure states.Comment: 4 pages, 1 encapsulated figure. In press on Phys. Rev.

Evidence on the Efficacy of School-Based Incentives for Healthy Living

We analyze the effects of a school-based incentive program on children's exercise habits. The program offers children an opportunity to win prizes if they walk or bike to school during prize periods. We use daily child-level data and individual fixed effects models to measure the impact of the prizes by comparing behavior during prize periods with behavior during non-prize periods. Variation in the timing of prize periods across different schools allows us to estimate models with calendardate fixed effects to control for day-specific attributes, such as weather and proximity to holidays. On average, we find that being in a prize period increases riding behavior by sixteen percent, a large impact given that the prize value is just six cents per participating student. We also find that winning a prize lottery has a positive impact on ridership over subsequent weeks; consider heterogeneity across prize type, gender, age, and calendar month; and explore differential effects on the intensive versus extensive margins.health; exercise; children; school; incentives; active commuting

XAI.it 2021 - Preface to the Second Italian Workshop on Explainable Artificial Intelligence

Artificial Intelligence systems are increasingly playing an increasingly important role in our daily lives. As their importance in our everyday lives grows, it is fundamental that the internal mechanisms that guide these algorithms are as clear as possible. It is not by chance that the recent General Data Protection Regulation (GDPR) emphasized the users' right to explanation when people face artificial intelligencebased technologies. Unfortunately, the current research tends to go in the opposite direction, since most of the approaches try to maximize the effectiveness of the models (e.g., recommendation accuracy) at the expense of the explainability and the transparency. The main research questions which arise from this scenario is straightforward: how can we deal with such a dichotomy between the need for effective adaptive systems and the right to transparency and interpretability? Several research lines are triggered by this question: building transparent intelligent systems, analyzing the impact of opaque algorithms on final users, studying the role of explanation strategies, investigating how to provide users with more control in the behavior of intelligent systems. XAI.it, the Italian workshop on Explainable AI, tries to address these research lines and aims to provide a forum for the Italian community to discuss problems, challenges and innovative approaches in the various sub-fields of XAI

On Interferometric Duality in Multibeam Experiments

We critically analyze the problem of formulating duality between fringe visibility and which-way information, in multibeam interference experiments. We show that the traditional notion of visibility is incompatible with any intuitive idea of complementarity, but for the two-beam case. We derive a number of new inequalities, not present in the two-beam case, one of them coinciding with a recently proposed multibeam generalization of the inequality found by Greenberger and YaSin. We show, by an explicit procedure of optimization in a three-beam case, that suggested generalizations of Englert's inequality, do not convey, differently from the two-beam case, the idea of complementarity, according to which an increase of visibility is at the cost of a loss in path information, and viceversa.Comment: 26 pages, 1 figure, substantial changes in the text, new material has been added in Section 3. Version to appear in J.Phys.