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An application of the general equation obtained in Part I to low critical temperature superconductors utilizing an "ad hoc" phononic theory is developed. Then, we arrive to a specific expression for the bounding energy as a function of temperature. The density of states of the electron pairs is calculated and used to obtain an equation for the critical magnetic field. This result is needed for determine the electrodynamical properties. Finally, we obtain the specific heat as a function of temperature and compare it to experimental data for Sn, and calculate its jump at Tc for eight superconductors., Comment: Second part of cond-mat/0403434 (New Theory of Supercondutivity). PDF file of 12 pags., 1 Figure and 1 Table

A general theory of superconductivity based on the pairing of electrons that belong to different electronic bands is presented. These electronic bands arise because of a symmetry breaking at the critical temperature in such a way that one electron sees the other as if its mass would be negative. This symmetry breaking leads also to an energy gap (centered round of the Fermi level) between the coupled electrons. Under the assumption that electric resistance is due to electron-phonon interaction, a general equation from which the fundamental properties of any metallic superconductor can be derived is also presented. In the frame of this theory, the electron-phonon interaction (or electric resistance) is cancelled out by the electron-electron interaction in the super-conducting state. Moreover, the Bardeen-Cooper- Schrieffer (BCS) theory is a particular case of our theory and equations, a matter, which leads to a better overall agreement with experimental data., Comment: 16 pages, 4 figures, Added figures

Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time approximations of the modeling diffusion processes are considered. On the other hand, there is a lack of simple estimating procedures based on higher order approximations. For standard diffusion models, that include additive and multiplicative noise components, we obtain the exact corrections to the empirical finite-time drift and diffusion coefficients, based on It\^o-Taylor expansions. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments, that furnish extra theoretical checks for that class of diffusive models. The theoretical predictions are compared with the numerical outcomes of some representative artificial time-series., Comment: 18 pages, 5 figures

This paper intends to meet recent claims for the attainment of more rigorous statistical methodology within the econophysics literature. To this end, we consider an econometric approach to investigate the outcomes of the log-periodic model of price movements, which has been largely used to forecast financial crashes. In order to accomplish reliable statistical inference for unknown parameters, we incorporate an autoregressive dynamic and a conditional heteroskedasticity structure in the error term of the original model, yielding the log-periodic-AR(1)-GARCH(1,1) model. Both the original and the extended models are fitted to financial indices of U. S. market, namely S&P500 and NASDAQ. Our analysis reveal two main points: (i) the log-periodic-AR(1)-GARCH(1,1) model has residuals with better statistical properties and (ii) the estimation of the parameter concerning the time of the financial crash has been improved., Comment: 17 pages, 4 figures, 12 tables, to appear in Europen Physical Journal B

In complex systems such as turbulent flows and financial markets, the dynamics in long and short time-lags, signaled by Gaussian and fat-tailed statistics, respectively, calls for a unified description. To address this issue we analyze a real dataset, namely, price fluctuations, in a wide range of temporal scales to embrace both regimes. By means of Kramers-Moyal (KM) coefficients evaluated from empirical time series, we obtain the evolution equation for the probability density function (PDF) of price returns. We also present consistent asymptotic solutions for the timescale dependent equation that emerges from the empirical analysis. From these solutions, new relationships connecting PDF characteristics, such as tail exponents, to parameters of KM coefficients arise. The results reveal a dynamical path that leads from Gaussian to fat-tailed statistics, furnishing insights on other complex systems where akin crossover is observed., Comment: 11 pages, 5 figures

This paper presents an empirical investigation of the intraday Brazilian stock market price fluctuations, considering q-Gaussian distributions that emerge from a non-extensive statistical mechanics. Our results show that, when returns are measured over intervals less than one hour, the empirical distributions are well fitted by q-Gaussians with exponential damped tails. Scaling behavior is also observed for these microscopic time intervals. We find that the time evolution of the distributions is according to a super diffusive q-Gaussian stationary process within a nonlinear Fokker-Planck equation. This regime breaks down due to the exponential fall-off of the tails, which in turn, governs the transient dynamics to the long-term macroscopic Gaussian regime. Our results suggest that this modeling provides a framework for the description of the dynamics of stock markets intraday price fluctuations., Comment: 17 pages, 11 figures and 1 table

We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive Wiener processes. While the former is modulated by the internal behavior of the system, the latter is purely exogenous. We focus on the stochastic dynamics of volatilities, but our model may also be suitable for other financial random variables exhibiting the mean reversion property. The generalized model contains, as particular cases, many early approaches in the literature of volatilities or, more generally, of mean-reverting financial processes. We analyze the long-time probability density function associated to the model defined through a It\^o-Langevin equation. We obtain a rich spectrum of shapes for the probability function according to the model parameters. We show that additive-multiplicative processes provide realistic models to describe empirical distributions, for the whole range of data., Comment: 8 pages, 3 figures

A General Theory of Superconductivity with points of view differing from those of the BCS Theory is presented in two parts. In the first part, a general equation for the superconductivity is obtained; based on the stable pairing of two electrons bound by a phonon for any type of superconductor material. This equation comes from a self consistent field calculation with a screening which is temperature dependent; showing that the total energy of the electron pair is constant and the local energy of the paired electrons is equal to that of the phonon in the range 0 K to critical temperature. A specific condition for the existence of the superconducting state is established allowing the prediction of the critical temperature. In the second part, the general equation is applied to low critical temperature superconductors where new results, in good agreement with experimental data, are calculated., Comment: Changes to abstract and introduction. File in PDF with 13 pages and 3 figures