Isotropic quantum walks on lattices and the Weyl equation

We present a thorough classification of the isotropic quantum walks on lattices of dimension $d=1,2,3$ for cell dimension $s=2$. For $d=3$ there exist two isotropic walks, namely the Weyl quantum walks presented in Ref. [G. M. D'Ariano and P. Perinotti, Phys. Rev. A 90, 062106 (2014)], resulting in the derivation of the Weyl equation from informational principles. The present analysis, via a crucial use of isotropy, is significantly shorter and avoids a superfluous technical assumption, making the result completely general.Comment: 16 pages, 1 figur

Chirality from quantum walks without quantum coin

Quantum walks (QWs) describe the evolution of quantum systems on graphs. An intrinsic degree of freedom---called the coin and represented by a finite-dimensional Hilbert space---is associated to each node. Scalar quantum walks are QWs with a one-dimensional coin. We propose a general strategy allowing one to construct scalar QWs on a broad variety of graphs, which admit embedding in Eulidean spaces, thus having a direct geometric interpretation. After reviewing the technique that allows one to regroup cells of nodes into new nodes, transforming finite spatial blocks into internal degrees of freedom, we prove that no QW with a two-dimensional coin can be derived from an isotropic scalar QW in this way. Finally we show that the Weyl and Dirac QWs can be derived from scalar QWs in spaces of dimension up to three, via our construction.Comment: 22 pages, 2 figure

The Italian expenditure in transport infrastructure: a survey

The aim of the paper is to analyse the most important quantitative data on Italian expenditures in transport infrastructures (investment and maintenance costs), linking the expenditure with traffic flows. The analysis concerns rail and road networks (both for national and local roads), over the last ten years, and a possible forecast for the next years, thanks to the official previsions of the “Objective Law”. The whole analysis is based on official data. The planned infrastructures will analyzed with taxonomical and cost – benefit approaches, in order to provide a ranking of priority. The results show how the planning of the investment expenditure is still based on different criteria than efficiency. So, the foreseen expenditure will not able to give relevant effects in order to improve the efficiency of the transport system and to obtain better allocative issues.transport expenditure; italy; infrastructure; investment

A high performance home in the Mediterranean climate: From the design principle to actual measurements

Experience developed in the northern European countries led, in the last decades, to standard and shared procedures for the design and construction of passive houses and similar high performance buildings. These approaches are specifically developed for cold climates, therefore cannot be directly applied to the Mediterranean climate, where substantially different climatic conditions must be challenged. The design and early monitoring of a customized zero energy house, located in Sicily, is proposed as an exemplary case study for the future generation of high performance and nearly-zero energy buildings in the Mediterranean area. The key role played by the control of heat gains, and the correct use of thermal mass is highlighted, showing similarities and differences with passive houses built in the North Europe. The measurements of energy and environmental performance of the building show the effectiveness of the response of the adopted design approach to the specific climatic conditions

Virtually Abelian Quantum Walks

We introduce quantum walks on Cayley graphs of non-Abelian groups. We focus on the easiest case of virtually Abelian groups, and introduce a technique to reduce the quantum walk to an equivalent one on an Abelian group with coin system having larger dimension. We apply the technique in the case of two quantum walks on virtually Abelian groups with planar Cayley graphs, finding the exact solution.Comment: 10 pages, 3 figure

Classical theories with entanglement

We investigate operational probabilistic theories where the pure states of every system are the vertices of a simplex. A special case of such theories is that of classical theories, i.e. simplicial theories whose pure states are jointly perfectly discriminable. The usual Classical Theory satisfies also local discriminability. However, simplicial theories---including the classical ones---can violate local discriminability, thus admitting of entangled states. First, we prove sufficient conditions for the presence of entangled states in arbitrary probabilistic theories. Then, we prove that simplicial theories are necessarily causal, and this represents a no-go theorem for conceiving non-causal classical theories. We then provide necessary and sufficient conditions for simplicial theories to exhibit entanglement, and classify their system-composition rules. We conclude proving that, in simplicial theories, an operational formulation of the superposition principle cannot be satisfied, and that---under the hypothesis of $n$-local discriminability---no mixed state admits of a purification. Our results hold also in the general case where the sets of states fail to be convex.Comment: The definitions of simplicial and classical theories have been relaxed, in order to include the non-convex cases; the results hold also in the non-convex cases. Improved and extended presentation. Added results on superposition and purification. Enhanced the 'Discussion and Conclusions' section. Minor corrections. Layout fixed and mention to Ref. [13] correcte

Alternative methods for measuring the influence of location in hedonic pricing models

The effects of location play a crucial role in the real estate market, encompassing aspects of accessibility and neighborhood. However, these are elements that are not directly measurable. There are traditional ways to consider location, usually through subjective measures based on professional experience, through proxy variables. Understanding these elements is vital for estimating real estate values, whether for legal, commercial, or tax purposes. Furthermore, seeking more objective options is a relevant issue to broaden the justification of estimated values and to enable the development of mass appraisal models. This article proposes and evaluates alternative solutions based on statistics, machine learning, and geostatistics to estimate location. A study was conducted using market data from Novo Hamburgo, southern Brazil, verifying the feasibility of the options presented. Satisfactory statistical results demonstrate the viability of the proposed approach