A discrete Schrodinger spectral problem and associated evolution equations

A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations are included and that the so called `inverse' class in the hierarchy is local. The whole class of related Darboux and Backlund transformations is also exhibited.Comment: 14 pages, LaTeX2

Berry Phase Quantum Thermometer

We show how Berry phase can be used to construct an ultra-high precision quantum thermometer. An important advantage of our scheme is that there is no need for the thermometer to acquire thermal equilibrium with the sample. This reduces measurement times and avoids precision limitations.Comment: Updated to published version. I. Fuentes previously published as I. Fuentes-Guridi and I. Fuentes-Schulle

Designing high-share 50% and 100% renewable energy scenarios for Ragusa by sustainable energy toolkit application

Increasing renewable energy production and integrating it into the current energy systems may lead to conditional solutions linked to the context of applications as well as regulatory and techno-socioeconomic issues. The PRISMI Plus toolkit is a powerful tool that can be improved to entail rural areas and energy islands for effective planning of the various renewable energy system scenarios associated with urban contexts. The target Flagship Case Study is Ragusa, a Municipality located in Southern Italy, analyzed with the EnergyPLAN software. The simulation and validation were carried out by the HOMER software. The input dataset was created jointly in collaboration with the Municipality, the updated Sustainable Energy Action Plan was inserted into the PRISMI Plus toolkit, and three transition scenarios based on different renewable energy uses were considered within the post-processing stage. For the baseline scenario, no green energy is considered and the whole electricity consumption is taken into account. In scenarios two and three, 50% and 100% renewable energy shares are secured through optimal investment in Photovoltaic (PV) panels, Wind Turbines (WT), and Battery Energy Storage (BES) technologies. From an economic point of view, it was concluded that the best scenario is the second one thanks to the increased technical capacity of the investment ratio compared with the two other scenarios, showing an energy price reduction of up to 10 %

A discrete time relativistic Toda lattice

Four integrable symplectic maps approximating two Hamiltonian flows from the relativistic Toda hierarchy are introduced. They are demostrated to belong to the same hierarchy and to examplify the general scheme for symplectic maps on groups equiped with quadratic Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flows are found for all the maps.Comment: 32 pages, LaTe

Cellular Automata and Ultra-Discrete Painlev\'e Equations

Starting from integrable cellular automata we present a novel form of Painlev\'e equations. These equations are discrete in both the independent variable and the dependent one. We show that they capture the essence of the behavior of the Painlev\'e equations organizing themselves into a coalescence cascade and possessing special solutions. A necessary condition for the integrability of cellular automata is also presented.Comment: 8 pages, plainTeX, 2 figure

Phenomenology of a light scalar: the dilaton

We make use of the language of non-linear realizations to analyze electro-weak symmetry breaking scenarios in which a light dilaton emerges from the breaking of a nearly conformal strong dynamics, and compare the phenomenology of the dilaton to that of the well motivated light composite Higgs scenario. We argue that -- in addition to departures in the decay/production rates into massless gauge bosons mediated by the conformal anomaly -- characterizing features of the light dilaton scenario (as well as other scenarios admitting a light CP-even scalar not directly related to the breaking of the electro-weak symmetry) are off-shell events at high invariant mass involving two longitudinally polarized vector bosons and a dilaton, and tree-level flavor violating processes. Accommodating both electro-weak precision measurements and flavor constraints appears especially challenging in the ambiguous scenario in which the Higgs and the dilaton fields strongly mix. We show that warped higgsless models of electro-weak symmetry breaking are explicit and tractable realizations of this limiting case. The relation between the naive radion profile often adopted in the study of holographic realizations of the light dilaton scenario and the actual dynamical dilaton field is clarified in the Appendix.Comment: 21 page

The lattice Schwarzian KdV equation and its symmetries

In this paper we present a set of results on the symmetries of the lattice Schwarzian Korteweg-de Vries (lSKdV) equation. We construct the Lie point symmetries and, using its associated spectral problem, an infinite sequence of generalized symmetries and master symmetries. We finally show that we can use master symmetries of the lSKdV equation to construct non-autonomous non-integrable generalized symmetries.Comment: 11 pages, no figures. Submitted to Jour. Phys. A, Special Issue SIDE VI