Liouville's Theorem from the Principle of Maximum Caliber in Phase Space

One of the cornerstones in non--equilibrium statistical mechanics (NESM) is Liouville's theorem, a differential equation for the phase space probability $\rho(q,p; t)$. This is usually derived considering the flow in or out of a given surface for a physical system (composed of atoms), via more or less heuristic arguments. In this work, we derive the Liouville equation as the partial differential equation governing the dynamics of the time-dependent probability $\rho(q, p; t)$ of finding a "particle" with Lagrangian $L(q, \dot{q}; t)$ in a specific point $(q, p)$ in phase space at time $t$, with $p=\partial L/\partial \dot{q}$. This derivation depends only on considerations of inference over a space of continuous paths. Because of its generality, our result is valid not only for "physical" systems but for any model depending on constrained information about position and velocity, such as time series

On nilspace systems and their morphisms

A nilspace system is a generalization of a nilsystem, consisting of a compact nilspace X equipped with a group of nilspace translations acting on X. Nilspace systems appear in different guises in several recent works, and this motivates the study of these systems per se as well as their relation to more classical types of systems. In this paper we study morphisms of nilspace systems, i.e., nilspace morphisms with the additional property of being consistent with the actions of the given translations. A nilspace morphism does not necessarily have this property, but one of our main results shows that it factors through some other morphism which does have the property. As an application we obtain a strengthening of the inverse limit theorem for compact nilspaces, valid for nilspace systems. This is used in work of the first and third named authors to generalize the celebrated structure theorem of Host and Kra on characteristic factors.Comment: 16 pages, 4 figures. Referee's comments incorporated, yielding several improvements in the exposition, especially in section 4. Accepted in Ergodic Theory and Dynamical System

Consecuencias de la internacionalización: la presencia del Islam en Europa

Màster Oficial d'Internacionalització, Facultat d'Economia i Empresa, Universitat de Barcelona, Curs: 2014-2015, Tutor: Xavier Fernández PonsEl objetivo de la presente obra, es la descripción de la situación de los musulmanes en Occidente tanto de facto como de iuris y la proposición de nuevas propuestas que favorezcan a la integración y a la convivencia pacífica. En cualquier caso, para los que aseguran que durante el Califato de al-Andalus existía una convivencia armónica y que, por lo tanto, esto ya está estudiado, es pertinente desmontarles la teoría de una convivencia pacífica y plural, ya que en al-Andalus se hablaba árabe y todo estaba sometido a la autoridad musulmana. Además, el pluralismo cultural está sometido a las nuevas reglas cambiantes de la globalización..

Mesoscopic entanglement induced by spontaneous emission in solid-state quantum optics

Implementations of solid-state quantum optics provide us with devices where qubits are placed at fixed positions in photonic or plasmonic one-dimensional waveguides. We show that solely by controlling the position ofthe qubits and withthe help of a coherent driving, collective spontaneous decay may be engineered to yield an entangled mesoscopic steady state. Our scheme relies on the realization of pure superradiant Dicke models by a destructive interference that cancels dipole-dipole interactions in one dimension

Statistical Behavior Of Domain Systems

We study the statistical behavior of two out of equilibrium systems. The first one is a quasi one-dimensional gas with two species of particles under the action of an external field which drives each species in opposite directions. The second one is a one-dimensional spin system with nearest neighbor interactions also under the influence of an external driving force. Both systems show a dynamical scaling with domain formation. The statistical behavior of these domains is compared with models based on the coalescing random walk and the interacting random walk. We find that the scaling domain size distribution of the gas and the spin systems is well fitted by the Wigner surmise, which lead us to explore a possible connection between these systems and the circular orthogonal ensemble of random matrices. However, the study of the correlation function of the domain edges, show that the statistical behavior of the domains in both gas and spin systems, is not completely well described by circular orthogonal ensemble, nor it is by other models proposed such as the coalescing random walk and the interacting random walk. Nevertheless, we find that a simple model of independent intervals describe more closely the statistical behavior of the domains formed in these systems.Comment: v2: minor change