Esperanto, graphic archetypes, biophilia. Esperanto, archetipi grafici, biofilia

Oggi è diffusa l’idea che il linguaggio iconico sia quello dell’era informatica, basato su un simbolo dal significato decifrabile con immediatezza a livello globale, tassello di un mondo virtuale che ha definitivamente traghettato l’umanità sulle rive di quel tanto atteso Esperanto voluto da Ludwik Lejzer Zamenhof, dagli effetti altamente benefici ma che nei giovani anche di medesimo idioma rende la parola parlata ormai quasi obsoleta, effetto collaterale questo ovviamente indesiderato. Tali tasselli iconico/informatici presenti nei nostri computer, tablet, cellulari ecc. vengono oggi percepiti in modo del tutto diverso da come lo erano i simboli fino agli anni ’70 e oltre. Sono degli enzimi o amminoacidi, degli agenti che svolgono svariate funzioni per noi. Ognuno di essi è un piccolo robot, un buon amico che ci tiene compagnia e che, all’occorrenza, ci viene in aiuto per trovare un’informazione, un’automobile in affitto, per effettuare una prenotazione, un piccolo divertimento, ecc. Ciò che qui interessa di questi potenti tasselli pro–attivi è, da un lato, il loro rapporto storico/ evolutivo significante–significato, cosa per la quale è necessario chiamare in campo l’Esperanto e gli archetipi grafici; dall’altro, capire se e come la città reale nel suo insieme possa trovarne giovamento, oltre quindi alla dimensione miope dei monitor small, large e x–large. In tal senso è utile operare un salto ontologico in direzione dell’ipotesi biofilica di Stephen Kellert, che possa aprire a possibili scenari di interazione tra simboli pro–attivi e territori non solo urbano/ambientali tout court, ma anche psicologico–comportamentali–percettivi, che stimolino a un uso fluido–dinamico della città e dei suoi spazi. Analizzare gli archetipi grafici − secondo una visione XYZ − ed usarne alcuni in tale chiave all’interno della biofilia, può rivelarsi utile a umanizzare la città trasformandola psicologicamente, con l’aiuto del verde, dell’arte e dell’architettura, in un organismo amico, nei cui tessuti resi vivi e non irritanti il fluido umano si senta protetto, avvolto e partecipe.Today we have the idea that the iconic language is that of the computer age, based on a symbol of decipherable meaning with a global immediacy, part of a virtual world that has definitively ferried humanity on the banks of that long–awaited Esperanto wanted by Ludwik Lejzer Zamenhof, with very beneficial effects, but that in young people even of the same language makes the spoken word almost obsolete, being this a collateral unwanted effect. These iconic/informatic dowels in our computers, tablets, mobile phones, etc. are perceived today in a completely different way from the symbols used until the 70s and beyond. They are enzymes or amino–acids, agents that perform various functions for us. Each of them is a small robot, a good friend who keeps us company and that, when necessary, helps us to find information, a rented car, to make a reservation, a little fun, etc. What is interesting here on these powerful proactive dowels is on the one hand their historical/evolutionary connection symbol–meaning, which is why it is necessary to call Esperanto and the graphic archetypes in the field, on the other to understand if and how the real city as a whole can find an advantage from them, out from the short–sighted dimension of small–large–xlarge monitors. In this sense it is useful to make an ontological leap towards the biophilic hypothesis of Stephen Kellert, that could open possible scenarios of interaction between proactive symbols and territories not only urban/environmental tout court, but also psychological–behavioral–perceptive, which stimulate a fluid–dynamic use of the city and its spaces. Analyzing graphic archetypes − according to an XYZ vision − and using some of them under this key within biophilia, can be useful to humanize the city, transforming it psychologically, with the help of green, art and architecture, into a friendly organism, in whose tissues rendered alive and not irritating, the human fluid feels protected, wrapped and participant

Ergodic Properties of the Quantum Ideal Gas in the Maxwell-Boltzmann Statistics

It is proved that the quantization of the Volkovyski-Sinai model of ideal gas (in the Maxwell-Boltzmann statistics) enjoys at the thermodynamical limit the properties of mixing and ergodicity with respect to the quantum canonical Gibbs state. Plus, the average over the quantum state of a pseudo-differential operator is exactly the average over the classical canonical measure of its Weyl symbol.Comment: 35 pages, LaTe

Typicality of recurrence for Lorentz gases

It is a safe conjecture that most (not necessarily periodic) two-dimensional Lorentz gases with finite horizon are recurrent. Here we formalize this conjecture by means of a stochastic ensemble of Lorentz gases, in which i.i.d. random scatterers are placed in each cell of a co-compact lattice in the plane. We prove that the typical Lorentz gas, in the sense of Baire, is recurrent, and give results in the direction of showing that recurrence is an almost sure property (including a zero-one law that holds in every dimension). A few toy models illustrate the extent of these results.Comment: 22 pages, 5 figure

Uniformly expanding Markov maps of the real line: exactness and infinite mixing

We give a fairly complete characterization of the exact components of a large class of uniformly expanding Markov maps of $\mathbb{R}$. Using this result, for a class of $\mathbb{Z}$-invariant maps and finite modifications thereof, we prove certain properties of infinite mixing recently introduced by the author.Comment: Final version to be published in Discrete and Continuous Dynamical Systems A. 47 pages, 5 figures. Labeling of appendices (and related wording) may differ from published versio

Exactness, K-property and infinite mixing

We explore the consequences of exactness or K-mixing on the notions of mixing (a.k.a. infinite-volume mixing) recently devised by the author for infinite-measure-preserving dynamical systems.Comment: Corrected reference to published version and fixed some typos, 15 page

Large deviations in quantum lattice systems: one-phase region

We give large deviation upper bounds, and discuss lower bounds, for the Gibbs-KMS state of a system of quantum spins or an interacting Fermi gas on the lattice. We cover general interactions and general observables, both in the high temperature regime and in dimension one.Comment: 30 pages, LaTeX 2

Infinite-horizon Lorentz tubes and gases: recurrence and ergodic properties

We construct classes of two-dimensional aperiodic Lorentz systems that have infinite horizon and are 'chaotic', in the sense that they are (Poincar\'e) recurrent, uniformly hyperbolic, ergodic, and the first-return map to any scatterer is $K$-mixing. In the case of the Lorentz tubes (i.e., Lorentz gases in a strip), we define general measured families of systems (\emph{ensembles}) for which the above properties occur with probability 1. In the case of the Lorentz gases in the plane, we define families, endowed with a natural metric, within which the set of all chaotic dynamical systems is uncountable and dense.Comment: Final version, to appear in Physica D (2011

Localization in infinite billiards: a comparison between quantum and classical ergodicity

Consider the non-compact billiard in the first quandrant bounded by the positive $x$-semiaxis, the positive $y$-semiaxis and the graph of $f(x) = (x+1)^{-\alpha}$, $\alpha \in (1,2]$. Although the Schnirelman Theorem holds, the quantum average of the position $x$ is finite on any eigenstate, while classical ergodicity entails that the classical time average of $x$ is unbounded.Comment: 9 page

More ergodic billiards with an infinite cusp

In a previous paper (nlin.CD/0107041) the following class of billiards was studied: For $f: [0, +\infty) \longrightarrow (0, +\infty)$ convex, sufficiently smooth, and vanishing at infinity, let the billiard table be defined by $Q$, the planar domain delimited by the positive $x$-semiaxis, the positive $y$-semiaxis, and the graph of $f$. For a large class of $f$ we proved that the billiard map was hyperbolic. Furthermore we gave an example of a family of $f$ that makes this map ergodic. Here we extend the latter result to a much wider class of functions.Comment: 13 pages, 4 figure