540 research outputs found
Generalized Pearson distributions for charged particles interacting with an electric and/or magnetic field
No full textThe linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to external electric and/or magnetic fields. We construct a Fokker-Planck approximation to the kinetic equations and derive the most general class of distributions for the given problem by discussing in detail some physically meallillgful cases. The equivalence with the transport theory of electrons in a phonon background is also discussed. (c) 2009 Elsevier B.V. All rights reserve
Boltzmann Configurational Entropy Revisited in the Framework of Generalized Statistical Mechanics
No full textAs known, a method to introduce non-conventional statistics may be realized by modifying the number of possible combinations to put particles in a collection of single-particle states. In this paper, we assume that the weight factor of the possible configurations of a system of interacting particles can be obtained by generalizing opportunely the combinatorics, according to a certain analytical function f{π}(n) of the actual number of particles present in every energy level. Following this approach, the configurational Boltzmann entropy is revisited in a very general manner starting from a continuous deformation of the multinomial coefficients depending on a set of deformation parameters {π}. It is shown that, when f{π}(n) is related to the solutions of a simple linear difference–differential equation, the emerging entropy is a scaled version, in the occupational number representation, of the entropy of degree (κ,r) known, in the framework of the information theory, as Sharma–Taneja–Mittal entropic form
Soliton-like behavior of a canonical quantum system obeying an exclusion-inclusion principle
No full textA justified modification of the real part of the complex non-linearity of a Schrödinger equation, recently proposed G. Kaniadakis, Phys. Rev. A 55 (1997) 941], allows us to obtain a new canonical quantum system obeying an exclusion-inclusion principle. The soliton solutions of this new effective Schrödinger equation are obtained in an implicit form
A kinetic derivation of a Butler-Volmer-like equation for the current-voltage characteristics in an adsorbing medium
No full textThe DC response of an electrochemical system submitted to an external difference of potential, is investigated by means of the Poisson-Nernst-Planck model. We suppose that only positive ions are injected into the electrochemical cell by the electrodes. For the injection mechanism we assume that it is well described by Nernst model, where the injected bulk density of ions depends on the difference of electric potential between the electrode and the bulk. Our goal is the determination of the current–voltage characteristics. We show that the functional dependence of the current density on the applied difference of potential is similar to that predicted by the Butler–Volmer equation relevant to an electrolytic cell submitted to an external difference of electric potential
Generalized kinetic equations for a system of interacting atoms and photons: theory and simulations
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