Papers by Massimo Coraddu
Non-extensive entropies and weak sensitivity at the edge of chaos
We analyze how different non-extensive, generalized entropic forms evolve in time for the logisti... more We analyze how different non-extensive, generalized entropic forms evolve in time for the logistic map at the onset of chaos, together with the associated sensitivity forms. Numerical evidence is given for the existence of an entropic index for which each entropy and the corresponding sensitivity increase linearly in time. The analogue of the Pesin equality is recovered when sensitivity to
Nuclear astrophysics in a q-environment
Fluctuations and dynamical collisions can be responsible of non standard distributions observed i... more Fluctuations and dynamical collisions can be responsible of non standard distributions observed in many astrophysical environments or astrophysical plasmas. In fact, since Coulomb collisions are the means to achieve equilibrium, plasmas are typically not in global thermodynamic equilibrium. We examine three different and linked problems whose solution is needed to determine parameters concerning evolution through metastable states of stars and
Theoretical Nuclear Physics in Italy - Proceedings of the 8th Conference on Problems in Theoretical Nuclear Physics, 2001
Energy and momentum of the elementary excitations become independent variables in medium: energy ... more Energy and momentum of the elementary excitations become independent variables in medium: energy and momentum statistical distributions are not identical. The momentum distribution and not the energy distribution is relevant for barrier penetration. The deviations of the momentum distribution from the Maxwell-Boltzmann energy distribution can be expressed in terms of the imaginary part of the self-energy of the quasi-particle. It is possible to obtain an effective Tsallis' distribution for the kinetic energy. These effects are different from static or dynamical screening and can have important consequences for reaction rates in stars.
Physica A: Statistical Mechanics and its Applications, 2004
We extend existing studies of weakly sensitive points within the framework of Tsallis non-extensi... more We extend existing studies of weakly sensitive points within the framework of Tsallis non-extensive thermodynamics to include weakly insensitive points at the edge of chaos. Analyzing tangent points of the logistic map we have verified that the generalized entropy with suitable entropic index q correctly describes the approach to the attractor.
Physica A: Statistical Mechanics and its Applications, 2003
The Super-Kamiokande best global fit, which includes data from SNO, Gallium and Chlorine experime... more The Super-Kamiokande best global fit, which includes data from SNO, Gallium and Chlorine experiments, results in a hep neutrino contribution to the signals that, even after oscillation, is greater than the SSM prediction. The solar hep neutrino flux that would yield this contribution is four times larger than the one predicted by the SSM. Recent detailed calculations exclude that the astrophysical factor S hep (0) could be wrong by such a large factor. Given the reliability of the temperature and densities profiles inside the Sun, this experimental result indicates that plasma effects are important for this reaction. We show that a slight enhancement of the high-energy tail, enhancement that is of the order of the deviations from the Maxwell-Boltzmann distribution expected in the solar core plasma, produces an increment of the hep rate of the magnitude required. We verified that the other neutrino fluxes remain compatible with experimental signals and SSM predictions. Better measurements of the high-energy tail of the neutrino spectrum would improve our understanding of reaction rates in the solar plasma.
Physica A: Statistical Mechanics and its Applications, 2006
Ensemble of initial conditions for nonlinear maps can be described in terms of entropy. This ense... more Ensemble of initial conditions for nonlinear maps can be described in terms of entropy. This ensemble entropy shows an asymptotic linear growth with rate K. The rate K matches the logarithm of the corresponding asymptotic sensitivity to initial conditions λ. The statistical formalism and the equality K = λ can be extended to weakly chaotic systems by suitable and corresponding generalizations of the logarithm and of the entropy. Using the logistic map as a test case we consider a wide class of deformed statistical description which includes Tsallis, Abe and Kaniadakis proposals. The physical criterion of finite-entropy growth K strongly restricts the suitable entropies. We study how large is the region in parameter space where the generalized description is useful.
Physica A: Statistical Mechanics and its Applications, 2002
We show that moderate deviations from the Maxwell-Boltzmann energy distribution can increase deut... more We show that moderate deviations from the Maxwell-Boltzmann energy distribution can increase deuterium reaction rates enough to contribute to the heating of Jupiter. These deviations are compatible with the violation of extensivity expected from temperature and density conditions inside Jupiter.
Non-resonant fusion cross-sections significantly higher than corresponding theoretical prediction... more Non-resonant fusion cross-sections significantly higher than corresponding theoretical predictions are observed in low-energy experiments with deuterated matrix target. Models based on thermal effects, electron screening, or quantum-effect dispersion relations have been proposed to explain these anomalous results: none of them appears to satisfactory reproduce the experiments. Velocity distributions are fundamental for the reaction rates and deviations from the Maxwellian limit could play a central role in explaining the enhancement. We examine two effects: an increase of the tail of the target Deuteron momentum distribution due to the Galitskii-Yakimets quantum uncertainty effect, which broadens the energy-momentum relation; and spatial fluctuations of the Debye-Hückel radius leading to an effective increase of electron screening. Either effect leads to larger reaction rates especially large at energies below a few keV, reducing the discrepancy between observations and theoretical expectations.
Complexity, Metastability and Nonextensivity - 31st Workshop of the International School of Solid State Physics, 2005
Numerical experiments support the interesting conjecture that statistical methods be applicable n... more Numerical experiments support the interesting conjecture that statistical methods be applicable not only to fully-chaotic systems, but also at the edge of chaos by using Tsallis' generalizations of the standard exponential and entropy. In particular, the entropy increases linearly and the sensitivity to initial conditions grows as a generalized exponential. We show that this conjecture has actually a broader validity by using a large class of deformed entropies and exponentials and the logistic map as test cases. * This work was partially supported by MIUR (Ministero dell'Istruzione, dell'Università e della Ricerca) under MIUR-PRIN-2003 project "Theoretical physics of the nucleus and the many-body systems".
Progress of Theoretical Physics, 2006
Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial condi... more Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial conditions is exponential with time: these two behaviors are related. Such relationship is the analogous of and under specific conditions has been shown to coincide with the Pesin identity. Numerical evidences support the proposal that the statistical formalism can be extended to the edge of chaos by using a specific generalization of the exponential and of the Boltzmann-Gibbs entropy. We extend this picture and a Pesin-like identity to a wide class of deformed entropies and exponentials using the logistic map as a test case. The physical criterion of finite-entropy growth strongly restricts the suitable entropies. The nature and characteristics of this generalization are clarified.
Physica A: Statistical Mechanics and its Applications, 2004
The Bochum experimental enhancement of the d+d fusion rate in a deuterated metal matrix at low in... more The Bochum experimental enhancement of the d+d fusion rate in a deuterated metal matrix at low incident energies is explained by the quantum broadening of the momentum-energy dispersion relation and consequent modification of the highmomentum tail of the distribution function from an exponential to a power-law.
Physica A: Statistical Mechanics and its Applications, 2004
Results of numerical simulations of fusion rate d(d,p)t, for low-energy deuteron beam, colliding ... more Results of numerical simulations of fusion rate d(d,p)t, for low-energy deuteron beam, colliding with deuterated metallic matrix (Raiola [1,2]) confirm analytical estimates given in Ref.
The European Physical Journal B, 2006
In fusion reactions, the Coulomb barrier selects particles from the high-momentum part of the dis... more In fusion reactions, the Coulomb barrier selects particles from the high-momentum part of the distribution. Therefore, small variations of the high-momentum tail of the velocity distribution can produce strong effects on fusion rates. In plasmas several potential mechanisms exist that can produce deviations from the standard Maxwell-Boltzmann distribution. Quantum broadening of the energy-momentum dispersion relation of the plasma quasi-particles modifies the high-momentum tail and could explain the fusion-rate enhancement observed in low-energy nuclear reaction experiments.
Brazilian Journal of Physics, 1999
The physics of nuclear reactions in stellar plasma is reviewed with special emphasis on the impor... more The physics of nuclear reactions in stellar plasma is reviewed with special emphasis on the importance of the velocity distribution of ions. Then the properties (density and temperature) of the weak-coupled solar plasma are analysed, showing that the ion velocities should deviate from the Maxwellian distribution and could be better described by a weakly-nonexstensive (|q − 1| < 0.02) Tsallis' distribution. We discuss concrete physical frameworks for calculating this deviation: the introduction of higher-order corrections to the diffusion and friction coefficients in the Fokker-Plank equation, the influence of the electric-microfield stochastic distribution on the particle dynamics, a velocity correlation function with long-time memory arising from the coupling of the collective and individual degrees of freedom. Finally, we study the effects of such deviations on stellar nuclear rates, on the solar neutrino fluxes, and on the pp neutrino energy spectrum, and analyse the consequences for the solar neutrino problem.
Brazilian Journal of Physics, 2009
Experimental measurements in terrestrial laboratory, space and astrophysical observations of vari... more Experimental measurements in terrestrial laboratory, space and astrophysical observations of variation and fluctuation of nuclear decay constants, measurements of large enhancements in fusion reaction rate of deuterons implanted in metals and electron capture by nuclei in solar core indicate that these processes depend on the environment where they take place and possibly also on the fluctuation of some extensive parameters and eventually on stellar energy production. Electron screening is the first important environment effect. We need to develop a treatment beyond the Debye-Hückel screening approach, commonly adopted within global thermodynamic equilibrium. Advances in the description of these processes can be obtained by means of q-thermostatistics and/or superstatistics for metastable states. This implies to handle, without ambiguities, the case q < 1.
Ultra high energy (UHE) photons can initiate electromagnetic showers in magnetic field. We analyz... more Ultra high energy (UHE) photons can initiate electromagnetic showers in magnetic field. We analyze the two processes that determine the development of the shower, $e^+ e^-$ pair creation and synchrotron radiation, and derive formulae for the angular distribution of the produced particles. These formulae are necessary to study the three-dimensional development of the shower.
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Papers by Massimo Coraddu