Classical microscopic theory of dispersion, emission and absorption of light in dielectrics

This paper is a continuation of a recent one in which, apparently for the first time, the existence of polaritons in ionic crystals was proven in a microscopic electrodynamic theory. This was obtained through an explicit computation of the dispersion curves. Here the main further contribution consists in studying electric susceptibility, from which the spectrum can be inferred. We show how susceptibility is obtained by the Green--Kubo methods of Hamiltonian statistical mechanics, and give for it a concrete expression in terms of time--correlation functions. As in the previous paper, here too we work in a completely classical framework, in which the electrodynamic forces acting on the charges are all taken into account, both the retarded forces and the radiation reaction ones. So, in order to apply the methods of statistical mechanics, the system has to be previously reduced to a Hamiltonian one. This is made possible in virtue of two global properties of classical electrodynamics, namely, the Wheeler--Feynman identity and the Ewald resummation properties, the proofs of which were already given for ordered system. The second contribution consists in formulating the theory in a completely general way, so that in principle it applies also to disordered systems such as glasses, or liquids or gases, provided the two general properties mentioned above continue to hold. A first step in this direction is made here by providing a completely general proof of the Wheeler--Feynman identity, which is shown to be the counterpart of a general causality property of classical electrodynamics. Finally it is shown how a line spectrum can appear at all in classical systems, as a counterpart of suitable stability properties of the motions, with a broadening due to a coexistence of chaoticity

Relaxation times and ergodicity properties in a realistic ionic--crystal model, and the modern form of the FPU problem

It is well known that Gibbs' statistical mechanics is not justified for systems presenting long-range interactions, such as plasmas or galaxies. In a previous work we considered a realistic FPU-like model of an ionic crystal (and thus with long-range interactions), and showed that it reproduces the experimental infrared spectra from 1000 K down to 7 K, provided one abandons the Gibbs identification of temperature in terms of specific kinetic energy, at low temperatures. Here we investigate such a model in connection with its ergodicity properties. The conclusion we reach is that at low temperatures ergodicity does not occur, and thus the Gibbs prescriptions are not dynamically justified, up to geological time scales. We finally give a preliminary result indicating how the so-called `nonclassical' q-statistics show up in the realistic ionic-crystal model. How to formulate a consistent statistical mechanics, with the corresponding suitable identification of temperature in such nonergodicity conditions, remains an open problem, which apparently constitutes the modern form of the FPU problem

The Fermi-Pasta-Ulam system as a model for glasses

Abstract We show that the standard Fermi-Pasta-Ulam system, with a suitable choice for the inter particle potential, constitutes a model for glasses, and indeed an extremely simple and manageable one. Indeed, it allows one to describe the landscape of the minima of the potential energy and to deal concretely with any one of them, determining the spectrum of frequencies and the normal modes. A relevant role is played by the harmonic energy E relative to a given minimum, i.e., the expansion of the Hamiltonian about the minimum up to second order. Indeed we find that there exists an energy threshold in E such that below it the harmonic energy E appears to be an approximate integral of motion for the whole observation time. Consequently, the system remains trapped near the minimum, in what may be called a vitreous or glassy state. Instead, for larger values of E the system rather quickly relaxes to a final equilibrium state. Moreover we find that the vitreous states present peculiar statistical behaviors, still involving the harmonic energy E. Indeed, the vitreous states are described by a Gibbs distribution with an effective Hamiltonian close to E and with a suitable effective inverse temperature. The final equilibrium state presents instead statistical properties which are in very good agreement with the Gibbs distribution relative to the full Hamiltonian of the system

Investigation of medicinal plants traditionally used as dietary supplements: a review on Moringa oleifera

Diet and nutrition are important factors in the promotion and maintenance of good health throughout the entire life course. A plant-based diet may be able to prevent and treat chronic diseases such as diabetes, heart disease and hypertension, obesity, chronic inflammation and cancer. Phytonutrient rich foods are found in traditional African diet which is mostly vegetarian, and most of these food plants are often used for medicinal purposes. This review focuses on a peculiar plant Moringa oleifera, called the “Miracle Tree”, considered to be one of nature's healthiest and most nutritious foods. Countless studies describe the benefits of Moringa leaves, pods, seeds and flowers. Its well documented role in prevention and treatment of chronic diseases is hypothesized here as a result of possible of cross-kingdom regulation by exogenous vegetal microRNAs and synergistic action of plant bioactive components on endogenous human microRNA regulation. The potential health impact of phytocomplexes from African dietary plants within the context of cross-kingdom and endogenous microRNA regulation on health improvement and the overall economic well-being of the continent is estimated to be enormous