Landauer and Thouless Conductance: a Band Random Matrix Approach

We numerically analyze the transmission through a thin disordered wire of finite length attached to perfect leads, by making use of banded random Hamiltonian matrices. We compare the Landauer and the Thouless conductances, and find that they are proportional to each other in the diffusive regime, while in the localized regime the Landauer conductance is approximately proportional to the square of the Thouless one. Fluctuations of the Landauer conductance were also numerically computed; they are shown to slowly approach the theoretically predicted value.Comment: 11 latex preprint pages with 6 ps figures, to appear in Journal de Physique I, May (1997

Dilation of states and processes in operational-probabilistic theories

This paper provides a concise summary of the framework of operational-probabilistic theories, aimed at emphasizing the interaction between category-theoretic and probabilistic structures. Within this framework, we review an operational version of the GNS construction, expressed by the so-called purification principle, which under mild hypotheses leads to an operational version of Stinespring's theorem.Comment: In Proceedings QPL 2014, arXiv:1412.810

A certain critical density property for invariant Harnack inequalities in H-type groups

We consider second order linear degenerate-elliptic operators which are elliptic with respect to horizontal directions generating a stratified algebra of H-type. Extending a result by Guti\'errez and Tournier for the Heisenberg group, we prove a critical density estimate by assuming a condition of Cordes-Landis type. We then deduce an invariant Harnack inequality for the non-negative solutions from a result by Di Fazio, Guti\'errez, and Lanconelli.Comment: 13 page

On the orientation of Roman towns in Italy

As is well known, several Roman sources report on the existence of a town foundation ritual, inherited from the Etruscans, which allegedly included astronomical references. However, the possible existence of astronomical orientations in the layout of Roman towns has never been tackled in a systematic way. As a first step in this direction, the orientation of virtually all Roman towns in Italy (38 cities) is studied here. Non-random orientation patterns emerge from these data, aiming at further research in this field.Comment: Archaeoastronomy/History of astronomy; 11 pages, 3 figure