Scaling behavior in the adiabatic Dicke Model

We analyze the quantum phase transition for a set of $N$-two level systems interacting with a bosonic mode in the adiabatic regime. Through the Born-Oppenheimer approximation, we obtain the finite-size scaling expansion for many physical observables and, in particular, for the entanglement content of the system.Comment: 4 pages, 3 figure

Scaling of Berry's Phase Close to the Dicke Quantum Phase Transition

We discuss the thermodynamic and finite size scaling properties of the geometric phase in the adiabatic Dicke model, describing the super-radiant phase transition for an $N$ qubit register coupled to a slow oscillator mode. We show that, in the thermodynamic limit, a non zero Berry phase is obtained only if a path in parameter space is followed that encircles the critical point. Furthermore, we investigate the precursors of this critical behavior for a system with finite size and obtain the leading order in the 1/N expansion of the Berry phase and its critical exponent

Finite-Size Scaling Exponents in the Dicke Model

We consider the finite-size corrections in the Dicke model and determine the scaling exponents at the critical point for several quantities such as the ground state energy or the gap. Therefore, we use the Holstein-Primakoff representation of the angular momentum and introduce a nonlinear transformation to diagonalize the Hamiltonian in the normal phase. As already observed in several systems, these corrections turn out to be singular at the transition point and thus lead to nontrivial exponents. We show that for the atomic observables, these exponents are the same as in the Lipkin-Meshkov-Glick model, in agreement with numerical results. We also investigate the behavior of the order parameter related to the radiation mode and show that it is driven by the same scaling variable as the atomic one.Comment: 4 pages, published versio

Nuclear halo and the coherent nuclear interaction

The unusual structure of Li11, the first halo nucleus found, is analyzed by the Preparata model of nuclear structure. By applying Coherent Nucleus Theory, we obtain an interaction potential for the halo-neutrons that rightly reproduces the fundamental state of the system.Comment: 9 pages Submitted to International Journal of Modern Physics E (IJMPE

Coherent QED, Giant Resonances and (e+e−)(e^{+}e^{-}) Pairs in High Energy Nucleus-Nucleus Collisions

We show that the coherent oscillations of the e.m. field induced by the collective quantum fluctuations of the nuclear matter field associated with the giant resonances, with frequencies $\omega_{A}\simeq 78A^{-{1/3}}$ MeV, give rise to a significant $(e^+e^-)$ pair production in high energy Heavy Ion collisions. The approximate parameterless calculation of such yield is in good agreement with recent experimental observations.Comment: 27 pages, 13 figure

Calibration of a Multichannel Water Vapor Raman Lidar through Noncollocated Operational Soundings: Optimization and Characterization of Accuracy and Variability

Abstract This paper presents a parametric automatic procedure to calibrate the multichannel Rayleigh–Mie–Raman lidar at the Institute for Atmospheric Science and Climate of the Italian National Research Council (ISAC-CNR) in Tor Vergata, Rome, Italy, using as a reference the operational 0000 UTC soundings at the WMO station 16245 (Pratica di Mare) located about 25 km southwest of the lidar site. The procedure, which is applied to both channels of the system, first identifies portions of the lidar and radiosonde profiles that are assumed to sample the same features of the water vapor profile, taking into account the different time and space sampling. Then, it computes the calibration coefficient with a best-fit procedure, weighted by the instrumental errors of both radiosounding and lidar. The parameters to be set in the procedure are described, and values adopted are discussed. The procedure was applied to a set of 57 sessions of nighttime 1-min-sampling lidar profiles (roughly about 300 h of measurements) covering the whole annual cycle (February 2007–September 2008). A calibration coefficient is computed for each measurement session. The variability of the calibration coefficients (∼10%) over periods with the same instrumental setting is reduced compared to the values obtained with the previously adopted, operator-assisted, and time-consuming calibration procedure. Reduction of variability, as well as the absence of evident trends, gives confidence both on system stability as well as on the developed procedure. Because of the definition of the calibration coefficient and of the different sampling between lidar and radiosonde, a contribution to the variability resulting from aerosol extinction and to the spatial and temporal variability of the water vapor mixing ratio is expected. A preliminary analysis aimed at identifying the contribution to the variability from these factors is presented. The parametric nature of the procedure makes it suitable for application to similar Raman lidar systems

Compact relaxations for polynomial programming problems

Reduced RLT constraints are a special class of Reformulation- Linearization Technique (RLT) constraints. They apply to nonconvex (both continuous and mixed-integer) quadratic programming problems subject to systems of linear equality constraints. We present an extension to the general case of polynomial programming problems and discuss the derived convex relaxation. We then show how to perform rRLT constraint generation so as to reduce the number of inequality constraints in the relaxation, thereby making it more compact and faster to solve. We present some computational results validating our approach