Egorov property in perturbed cat map

We study the time evolution of the quantum-classical correspondence (QCC) for the well known model of quantised perturbed cat maps on the torus in the very specific regime of semi-classically small perturbations. The quality of the QCC is measured by the overlap of classical phase-space density and corresponding Wigner function of the quantum system called quantum-classical fidelity (QCF). In the analysed regime the QCF strongly deviates from the known general behaviour in particular it decays faster then exponential. Here we study and explain the observed behavior of the QCF and the apparent violation of the QCC principle.Comment: 12 pages, 7 figure

Deterministic spin models with a glassy phase transition

We consider the infinite-range deterministic spin models with Hamiltonian $H=\sum_{i,j=1}^N J_{i,j}\sigma_i\sigma_j$, where $J$ is the quantization of a chaotic map of the torus. The mean field (TAP) equations are derived by summing the high temperature expansion. They predict a glassy phase transition at the critical temperature $T\sim 0.8$.Comment: 8 pages, no figures, RevTex forma

Relative entropy via non-sequential recursive pair substitutions

The entropy of an ergodic source is the limit of properly rescaled 1-block entropies of sources obtained applying successive non-sequential recursive pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D. Benedetto, E. Caglioti and D. Gabrielli 2006 Jour. Stat. Mech. Theo. Exp. 09 doi:10.1088/1742.-5468/2006/09/P09011). In this paper we prove that the cross entropy and the Kullback-Leibler divergence can be obtained in a similar way.Comment: 13 pages , 2 figure

Pairing, crystallization and string correlations of mass-imbalanced atomic mixtures in one-dimensional optical lattices

We numerically determine the very rich phase diagram of mass-imbalanced binary mixtures of hardcore bosons (or equivalently -- fermions, or hardcore-Bose/Fermi mixtures) loaded in one-dimensional optical lattices. Focusing on commensurate fillings away from half filling, we find a strong asymmetry between attractive and repulsive interactions. Attraction is found to always lead to pairing, associated with a spin gap, and to pair crystallization for very strong mass imbalance. In the repulsive case the two atomic components remain instead fully gapless over a large parameter range; only a very strong mass imbalance leads to the opening of a spin gap. The spin-gap phase is the precursor of a crystalline phase occurring for an even stronger mass imbalance. The fundamental asymmetry of the phase diagram is at odds with recent theoretical predictions, and can be tested directly via time-of-flight experiments on trapped cold atoms.Comment: 4 pages, 4 figures + Supplementary Materia

Quantum-classical correspondence on compact phase space

We propose to study the $L^2$-norm distance between classical and quantum phase space distributions, where for the latter we choose the Wigner function, as a global phase space indicator of quantum-classical correspondence. For example, this quantity should provide a key to understand the correspondence between quantum and classical Loschmidt echoes. We concentrate on fully chaotic systems with compact (finite) classical phase space. By means of numerical simulations and heuristic arguments we find that the quantum-classical fidelity stays at one up to Ehrenfest-type time scale, which is proportional to the logarithm of effective Planck constant, and decays exponentially with a maximal classical Lyapunov exponent, after that time.Comment: 26 pages. 9 figures (31 .epz files), submitted to Nonlinearit

Sustainable PHBV/CuS Composite Obtained from Waste Valorization for Wastewater Purification by Visible Light-Activated Photocatalytic Activity

The persistency of antimicrobial compounds in the water cycle accelerates the issue of antimicrobial resistance. Therefore, effective wastewater remediation approaches, which can be implemented on a large scale, are urgently required. This study aims at preparing a sustainable organic/inorganic composite material that can photo-catalyze the degradation of organic pollutants in wastewater by using visible light. Specifically, films and porous composites are composed of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) as supporting material, and copper sulfide (CuS) as active photocatalyst. It is noteworthy that the proposed composite can be fully produced from waste valorization, since PHBV is a polymer, which can be obtained by fermentation of vegetable wastes, and CuS is synthesized from industrial sulfur wastes. The produced composites show remarkable capabilities in the photodegradation of tetracycline and methylene blue, selected as model organic pollutants. Moreover, the PHBV/CuS composites can be reused multiple times with minimal loss in photocatalytic efficiency. The suggested approach is not only sustainable and cost-effective, but also solves issues occurring in the application of the photodegradation techniques currently reported, such as the consumption of fossil-based chemicals and photocatalyst removal from the purified water using with expensive procedures

Quantum response of weakly chaotic systems

Chaotic systems, that have a small Lyapunov exponent, do not obey the common random matrix theory predictions within a wide "weak quantum chaos" regime. This leads to a novel prediction for the rate of heating for cold atoms in optical billiards with vibrating walls. The Hamiltonian matrix of the driven system does not look like one from a Gaussian ensemble, but rather it is very sparse. This sparsity can be characterized by parameters $s$ and $g$ that reflect the percentage of large elements, and their connectivity respectively. For $g$ we use a resistor network calculation that has direct relation to the semi-linear response characteristics of the system.Comment: 7 pages, 5 figures, expanded improved versio

New sustainable routes for gas separation membranes: The properties of poly(hydroxybutyrate-co-hydroxyvalerate) cast from green solvents

The gas separation performance of biopolymers is still scarcely characterized, mostly because of their poor thermomechanical properties and high crystallinity which is associated to low permeability. In this work we characterize the gas transport in a poly(hydroxybutyrate-co-hydroxyvalerate) (PHBV) random copolymer, that has a relatively low crystallinity and good mechanical properties, combined with a renewable origin, biodegradability and biocompatibility. In the study we also compared several solvents for membrane casting, with different toxicity levels. We found that dimethyl carbonate allows the production of polymer films with transport properties similar to those obtained with the more toxic CHCl3, and it leads also to stable crystallinity of the samples over time. PHBV films show a size-sieving gas separation behaviour, as the permeability decreases significantly with the gas kinetic diameter. However, the strong energetic interactions of CO2 with the polymer matrix, confirmed by the Flory-Huggins model, induce a marked solubility-driven CO2/N2 and CO2/CH4 selectivity, which could make the material potentially interesting for CO2 removal processes

A Multi-Frequency Investigation of Air-To-Ground Urban Propagation Using a GPU-based Ray Launching Algorithm

Unmanned Aerial Vehicles (UAV), also known as “drones”, are attracting increasing attention as enablers for many technical applications and services, and this trend is likely to continue in the next future. When compared to conventional terrestrial communications, those making use of UAVs as base- or relay-stations can definitely be more useful and flexible in reaction to specific events, like natural disasters and terrorist attacks. Among the many and different fields, UAV enabled communications emerge as one of the most promising solutions for next-generation mobile networks, with a special focus on the extension of coverage and capacity of mobile radio networks. Motivated by the air-to-ground (A2G) propagation conditions which are likely to be different than those experienced by traditional ground communication systems, this paper aims at investigating the narrowband properties of the air-to-ground channel for 5G communications and beyond by means of GPU accelerated ray launching simulations. Line of sight probability as well as path loss exponent and shadowing standard deviations are analysed for different UAV flight levels, frequencies and dense urban scenarios, and for different types of on board antennas. Thanks to the flexibility of the ray approach, the role played by the different electromagnetic interactions, namely reflection, diffraction and diffuse scattering, in the air-to-ground propagation process is also investigated. Computation time is reported as well to show that designing UAV communication networks and optimising their performances in a fast and reliable manner, might avoid exhausting – multiple - measurement campaigns

On the Form Factor for the Unitary Group

We study the combinatorics of the contributions to the form factor of the group U(N) in the large $N$ limit. This relates to questions about semiclassical contributions to the form factor of quantum systems described by the unitary ensemble.Comment: 35 page