A Converse Hawking-Unruh Effect and dS^2/CFT Correspondance

Given a local quantum field theory net A on the de Sitter spacetime dS^d, where geodesic observers are thermalized at Gibbons-Hawking temperature, we look for observers that feel to be in a ground state, i.e. particle evolutions with positive generator, providing a sort of converse to the Hawking-Unruh effect. Such positive energy evolutions always exist as noncommutative flows, but have only a partial geometric meaning, yet they map localized observables into localized observables. We characterize the local conformal nets on dS^d. Only in this case our positive energy evolutions have a complete geometrical meaning. We show that each net has a unique maximal expected conformal subnet, where our evolutions are thus geometrical. In the two-dimensional case, we construct a holographic one-to-one correspondence between local nets A on dS^2 and local conformal non-isotonic families (pseudonets) B on S^1. The pseudonet B gives rise to two local conformal nets B(+/-) on S^1, that correspond to the H(+/-)-horizon components of A, and to the chiral components of the maximal conformal subnet of A. In particular, A is holographically reconstructed by a single horizon component, namely the pseudonet is a net, iff the translations on H(+/-) have positive energy and the translations on H(-/+) are trivial. This is the case iff the one-parameter unitary group implementing rotations on dS^2 has positive/negative generator.Comment: The title has changed. 38 pages, figures. To appear on Annales H. Poincare

Singular vector expansion functions for finite methods

This paper describes the fundamental properties of new singular vector bases that incorporate the edge conditions in curved triangular elements. The bases are fully compatible with the interpolatory or hierarchical high-order regular vector bases used in adjacent elements. Several numerical results confirm the faster convergence of these bases on wedge problems and the capability to model regular fields when the singularity is not excite

Singular Higher-Order Complete Vector Bases for Finite Methods

This paper presents new singular curl- and divergence- conforming vector bases that incorporate the edge conditions. Singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester-Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. The curl (divergence) conforming singular bases guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modeling of the curl (divergence), and removal of spurious modes (solutions). These singular high-order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems. Sample numerical results confirm the faster convergence of these bases on wedge problems

Natural Energy Bounds in Quantum Thermodynamics

Given a stationary state for a noncommutative flow, we study a boundedness condition, depending on a positive parameter beta, which is weaker than the KMS equilibrium condition at inverse temperature beta. This condition is equivalent to a holomorphic property closely related to the one recently considered by Ruelle and D'Antoni-Zsido and shared by a natural class of non-equilibrium steady states. Our holomorphic property is stronger than the Ruelle's one and thus selects a restricted class of non-equilibrium steady states. We also introduce the complete boundedness condition and show this notion to be equivalent to the Pusz-Woronowicz complete passivity property, hence to the KMS condition. In Quantum Field Theory, the beta-boundedness condition can be interpreted as the property that localized state vectors have energy density levels increasing beta-subexponentially, a property which is similar in the form and weaker in the spirit than the modular compactness-nuclearity condition. In particular, for a Poincare' covariant net of C*-algebras on the Minkowski spacetime, the beta-boundedness property, for beta greater equal than 2 pi, for the boosts is shown to be equivalent to the Bisognano-Wichmann property. The Hawking temperature is thus minimal for a thermodynamical system in the background of a Rindler black hole within the class of beta-holomorphic states. More generally, concerning the Killing evolution associated with a class of stationary quantum black holes, we characterize KMS thermal equilibrium states at Hawking temperature in terms of the boundedness property and the existence of a translation symmetry on the horizon.Comment: 28 pages, LaTeX. Minor modifications in the abstract, to appear in Commun. Math. Phy

Investment in Tourism Market: A Dynamic Model of Differentiated Oligopoly

We present a theoretical model in tourism economics, assuming that the market for tourism is an oligopoly with differentiated products. Destinations (i.e., countries, regions, sites or even firms) can invest in order to improve their carrying capacity that can be interpreted as the stock of physical, natural or cultural resources. Tourism flows yield current revenues, but they are usually detrimental for the cultural or natural resource stock over time. We find the solution of the dynamic model, and in particular we find the open-loop Nash equilibrium of the game among the destinations, under alternative settings, depending on whether the arrivals are exogenous or endogenous, and depending on whether the degree of differentiation among destinations is exogenous or endogenous. The model is rather general, and it can provide answers to different specific questions, like the choice between mass- vs. elite-tourism development strategies; the effect of the number of competing products upon profits; the optimal degree of product differentiation.Tourism, Differentiated games, Reservation price

Intellectual Property, Competition and Growth: An Introduction

This paper introduces the monographic issue of Rivista di Politica Economica on “Intellectual Property, Competition, and Growth”. It presents the twelve contributions selected after a Callfor-Papers. The contributions deal with different facets of the protection of intellectual property rights and analyse micro- and macro-economic consequences of different degree of intellectual property protection, especially as concerns firm competition and macroeconomic growth performance.

The multi-path Traveling Salesman Problem with stochastic travel costs

Given a set of nodes, where each pair of nodes is connected by several paths and each path shows a stochastic travel cost with unknown distribution, the multipath Traveling Salesman Problem with stochastic travel costs aims at finding an expected minimum Hamiltonian tour connecting all nodes. Under a mild assumption on the unknown probability distribution a deterministic approximation of the stochastic problem is given. The comparison of such approximation with a Montecarlo simulation shows both the accuracy and the eciency of the deterministic approximation, with a mean percentage gap around 2% and a reduction of the computational times of two orders of magnitude