Elementary test for non-classicality based on measurements of position and momentum

We generalise a non-classicality test described by Kot et al. [Phys. Rev. Lett. 108, 233601 (2010)], which can be used to rule out any classical description of a physical system. The test is based on measurements of quadrature operators and works by proving a contradiction with the classical description in terms of a probability distribution in phase space. As opposed to the previous work, we generalise the test to include states without rotational symmetry in phase space. Furthermore, we compare the performance of the non-classicality test with classical tomography methods based on the inverse Radon transform, which can also be used to establish the quantum nature of a physical system. In particular, we consider a non-classicality test based on the so-called filtered back-projection formula. We show that the general non-classicality test is conceptually simpler, requires less assumptions on the system and is statistically more reliable than the tests based on the filtered back-projection formula. As a specific example, we derive the optimal test for a quadrature squeezed single photon state and show that the efficiency of the test does not change with the degree of squeezing

Effective Dynamics of Extended Fermi Gases in the High-Density Regime

We study the quantum evolution of many-body Fermi gases in three dimensions, in arbitrarily large domains. We consider both particles with non-relativistic and with relativistic dispersion. We focus on the high-density regime, in the semiclassical scaling, and we consider a class of initial data describing zero-temperature states. In the non-relativistic case we prove that, as the density goes to infinity, the many-body evolution of the reduced one-particle density matrix converges to the solution of the time-dependent Hartree equation, for short macroscopic times. In the case of relativistic dispersion, we show convergence of the many-body evolution to the relativistic Hartree equation for all macroscopic times. With respect to previous work, the rate of convergence does not depend on the total number of particles, but only on the density: in particular, our result allows us to study the quantum dynamics of extensive many-body Fermi gases

A Supersymmetric Hierarchical Model for Weakly Disordered 3d Semimetals

In this paper, we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of disorder. We use rigorous renormalization group methods and supersymmetry to compute the correlation functions of the system. We prove algebraic decay of the two-point correlation function, compatible with delocalization. A main technical ingredient is the multiscale analysis of massless bosonic Gaussian integrations with purely imaginary covariances, performed via iterative stationary phase expansions

Microwave-Assisted Synthesis, Optical and Theoretical Characterization of Novel 2-(imidazo[1,5-a]pyridine-1-yl)pyridinium Salts

In the last few years, imidazo[1,5-a]pyridine scaffolds and derivatives have attracted growing attention due to their unique chemical structure and optical behaviors. In this work, a series of pyridylimidazo[1,5-a]pyridine derivatives and their corresponding pyridinium salts were synthesized and their optical properties investigated to evaluate the effect of the quaternization on the optical features both in solution and polymeric matrix. A critical analysis based on the spectroscopic data, chemical structures along with density functional theory calculation is reported to address the best strategies to prevent aggregation and optimize the photophysical properties. The obtained results describe the relationship between chemical structure and optical behaviors, highlighting the role of pendant pyridine. Finally, the presence of a positive charge is fundamental to avoid any possible aggregation process in polymeric films

Supersymmetric Cluster Expansions and Applications to Random Schrodinger Operators

We study discrete random Schr\"odinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green's function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.Comment: 36 pages, 1 figur

Biological enhancement of graft-tunnel healing in anterior cruciate ligament reconstruction

The sites where graft healing occurs within the bone tunnel and where the intra-articular ligamentization process takes place are the two most important sites of biological incorporation after anterior cruciate ligament (ACL) reconstruction, since they help to determine the mechanical behavior of the femur-ACL graft-tibia complex. Graft-tunnel healing is a complex process influenced by several factors, such as type of graft, preservation of remnants, bone quality, tunnel length and placement, fixation techniques and mechanical stress. In recent years, numerous experimental and clinical studies have been carried out to evaluate potential strategies designed to enhance and optimize the biological environment of the graft-tunnel interface. Modulation of inflammation, tissue engineering and gene transfer techniques have been applied in order to obtain a direct-type fibrocartilaginous insertion of the ACL graft, similar to that of native ligament, and to accelerate the healing process of tendon grafts within the bone tunnel. Although animal studies have given encouraging results, clinical studies are lacking and their results do not really support the use of the various strategies in clinical practice. Further investigations are therefore needed to optimize delivery techniques, therapeutic concentrations, maintenance of therapeutic effects over time, and to reduce the risk of undesirable effects in clinical practice