Roberto Beneduci

NEUMARK'S OPERATORS AND SHARP RECONSTRUCTIONS

Given a commutative POV measure on the Borel σ-algebra of the reals it is possible to construct a PV measure (the sharp reconstruction of F) such that the outcomes of the measurement of F can be interpreted as the random diffusion of the outcomes of the measurement of E. On the other hand Neumarks theorem ensures the existence of an extended Hilbert space and of a PV measure such that for every . We consider the projection of the self-adjoint operator corresponding to E+ and the self-adjoint operator A corresponding to the sharp reconstruction E and show the existence of a function G: [0,1] → [0,1] such that . An example for which the last relation can be inverted is shown.

On the unavoidability of the interpretations of quantum mechanics

on the interpre-tation of quantum mechanics. The central theme of the debate was a criticism to the (alsorecent) presence in the literature of voluminous discussions about the interpretation ofquantum mechanics. That there still exists such discussions is what van Kampen calls thescandal of quantum mechanics.We claim that a weak point in the debate was a lack of a de nition of the term inter-pretation. In the present note, we would like to make that meaning precise and to showhow such a clari cation is necessary in order to avoid misunderstandings. The concept ofinterpretation plays a key role in the history of physics, so we hope the present analysismight be helpful to the student.Max Jammer,

A note on the relationship between localization and the norm-1 property

This paper focuses on the problem of localization in quantum mechanics. It is well known that it is not possible to define a localization observable for the photon by means of projection-valued measures, or conversely, that it is possible by using positive operator-valued measures. On the other hand, projection-valued measures imply a kind of localization which is stronger than that implied by positive operator-valued measures. It has been claimed that the norm-1 property would in some sense reduce the gap between the two kinds of localizations. We give a necessary condition for the norm-1 property and show that it is not satisfied by several important localization observables.

Uniform Continuity of POVMs

Recently a characterization of uniformly continuous POVMs and a necessary condition for a uniformly continuous POVM F to have the norm-1 property have been provided. Moreover it was proved that in the commutative case, uniform continuity corresponds to the existence of a Feller Markov kernel. We apply such results to the analysis of some relevant physical examples; i.e., the phase space localization observables, the unsharp phase observable and the unsharp number observable of which we study the uniform continuity, the norm-1 property and the existence of a Feller Markov kernel.

Self-decoherence criterion of consistency for quantum histories

We introduce a meaningful consistency criterion, called self-decoherence, for families of 2-event quantum histories, which implies weak decoherence. We show that a condition of heredity, stemming from Ludwigs interpretation of density matrix, is satisfied by self-decoherence. On the contrary, usual consistency criteria are not hereditary.

Extended Hydrodynamical Models for Charge Transport in Si

In this paper we present a hierarchy of extended hydrodynamical models for electron transport in Silicon, which differ from each other for the number of scalar and vector moments of the electron distribution function used as state variables. The closure of the moment equations is achieved by means of the Maximum Entropy Principle. The main scattering mechanisms between electrons and phonons are taken into account. An application to the case of bulk Silicon is presented.