Deformed logarithms and entropies

By solving a differential-functional equation inposed by the MaxEnt principle we obtain a class of two-parameter deformed logarithms and construct the corresponding two-parameter generalized trace-form entropies. Generalized distributions follow from these generalized entropies in the same fashion as the Gaussian distribution follows from the Shannon entropy, which is a special limiting case of the family. We determine the region of parameters where the deformed logarithm conserves the most important properties of the logarithm, and show that important existing generalizations of the entropy are included as special cases in this two-parameter class.Comment: Presented at next2003, Second Sardinian International Conference on News and Expectations in Thermostatistics, Villasimius (Cagliari) Italy, 21st-28th September 2003. In press Physica A (2004). Elsevier LaTeX macros, 11 pages, 1 figur

Non-Markovian effects in the solar neutrino problem

The solar core, because of its density and temperature, is not a weakly-interacting or a high-temperature plasma. Collective effects have time scales comparable to the average time between collisions, and the microfield distribution influences the particle dynamics. In this conditions ion and electron diffusion is a non-Markovian process, memory effects are present and the equilibrium statistical distribution function differs from the Maxwellian one. We show that, even if the deviations from the standard velocity distribution that are compatible with our present knowledge of the solar interior are small, they are sufficient to sensibly modify the sub-barrier nuclear reaction rates. The consequent changes of the neutrino fluxes are comparable to the flux deficits that constitute the solar neutrino problem.Comment: 4 pages, to appear in the Proceedings of Nuclei in the Cosmos

Thermal distributions in stellar plasmas, nuclear reactions and solar neutrinos

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.Comment: ReVTeX, 23 pages, 3 figures, to appear in the special issue (Nonextensive statistical mechanics and thermodynamics) of the Brazilian Journal of Physic

Hadron wave functions and the issue of nucleon deformation

Using gauge invariant hadronic two- and three- density correlators we extract information on the spatial distributions of quarks in hadrons, and on hadron shape and multipole moments within quenched lattice QCD. Combined with the calculation of N to Delta transition amplitudes the issue of nucleon deformation can be addressed.Comment: 4 pages, 7 figures. Talk presented at the PANIC02 conference, Sept. 30 - Oct. 4, 2002, Osaka, Japan. Discussion of the N to Delta results modifie

Modified Debye-Huckel Electron Shielding and Penetration Factor

Screened potential, modified by non standard electron cloud distributions responsible for the shielding effect on fusion of reacting nuclei in astrophysical plasmas, is derived. The case of clouds with depleted tails in space coordinates is discussed. The modified screened potential is obtained both from statistical mechanics arguments based on fluctuations of the inverse of the Debye-Huckel radius and from the solution of a Bernoulli equation used in generalized statistical mechanics. Plots and tables useful in evaluating penetration probability at any energy are provided.Comment: 9 pages, 3 figures, 3 table

Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics

A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging differential-functional equation yields a two-parameter class of generalized logarithms, from which entropies and power-law distributions follow: these distributions could be relevant in many anomalous systems. Within the specified range of parameters, these entropies possess positivity, continuity, symmetry, expansibility, decisivity, maximality, concavity, and are Lesche stable. The Boltzmann-Shannon entropy and some one parameter generalized entropies already known belong to this class. These entropies and their distribution functions are compared, and the corresponding deformed algebras are discussed.Comment: Version to appear in PRE: about 20% shorter, references updated, 13 PRE pages, 3 figure

High-energy neutrino conversion into electron-W pair in magnetic field and its contribution to neutrino absorption

We calculate the conversion rate of high-energy neutrinos propagating in constant magnetic field into an electron-W pair (nu -> W + e) from the imaginary part of the neutrino self-energy. Using the exact propagators in constant magnetic field, the neutrino self-energy has been calculated to all order in the field within the Weinberg-Salam model. We obtain a compact formula in the limit of B << Bcr = m^2/e. We find that above the process threshold Eth \~ 2.2 10^16 (Bcr / B) eV this contribution to the absorption of neutrinos yields an asymptotic absorption length ~ 1.1 (Bcr / B)^2 (10^{16} eV / E) meters.Comment: 10 pages in RevTeX, 2 figures; published version: two typos corrected, one reference adde

Nuclear physics inputs needed for geo-neutrino studies

Geo-neutrino studies are based on theoretical estimates of geo-neutrino spectra. We propose a method for a direct measurement of the energy distribution of antineutrinos from decays of long-lived radioactive isotopes.Comment: 6 pages, 3 figures. Proceedings of the International Conference on Topics in Astroparticle and Underground Physics (TAUP) 2007, Sendai, Japan, September 11-15, 2007. To appear in Journal of Physics: Conference Serie