Suchergebnisse

On étudie l'espace de configuration d'un point en mouvement dans un champ électromagnétique généralisé. Fonction de Lagrange L et Hamiltonienne H. Équations de mouvements. Interprétation géométrique des équations L = 1 et H = 1 .

Defining generalised functions products by analytic continuation, a two-point function whose mass distribution is positive may be used in the non linear spinor theory. As an application, we show that in an approximation where only strong interactions are considered — so that no imaginary parts have to be neglected, correct values for the π and η meson masses (and eventually, using enough parameters, for the meson nucleon coupling constants) may be obtained, in the first order of the new Tamm-Dancoff method, if the mass distribution is positive ; if not, it seems that the contribution of the negative part must be negligible.

In this final part we apply the formal techniques introduced in parts I and II to the Lorentz transformations of the asymptotic master equations. The different forms of the collision operator are also briefly discussed.

Nonequilibrium fluctuating hydrodynamic equations are derived by a generalised Chapman-Enskog development applied to a previously de¬ duced nonlinear Langevin-Boltzmann equation. The long range character of the correlations in the hydrodynamic subspace is established.

The superoperator transformation theory developed by the Brussels school is applied to a simple quantum-mechanical system : the one-boson Lee model. The existence of a diagonalising transformation for this model permits the solution of dynamical problems such as that of induced emission and the construction of explicit matrix representations for asymptotic and dressing operators of the theory.

Abstract. — The collision operator is calculated for a system representing an infinite one-dimensional lattice in a uniform external field. Using its spectral properties we construct the unitary transformation which diago-nalizes the von Neumann operator. We follow the theory developed by the Brussels group in studying the dissipative properties of quantum systems.

Working within the formalism developed by Professor I. Prigogine and his coworkers, this paper examines both the perturbation series obtained by iterating the resolvent equation and the irreducible operators introduced by this means. It is shown that the series can be regarded as asymptotic in a certain sense but that this interpretation is not useful for long time behaviour. Instead of performing the usual resummation of the series it is shown that the irreducible operators can be defined in an entirely rigorous way independent of the series expansion. The advantages of this approach and its connection with the usual procedure are pointed out.

La forme générale de l'équation cinétique d'un plasma instable dans l'approximation des anneaux est donnée. Le calcul du terme des interactions est basé sur les propriétés des fonctions propres de l'opérateur de Vlassov linéarisé.
L'expression générale de la fonction de correlation de densité est calculée.

This part is devoted to the asymptotic theory of the exact master equations which were discussed in Part I.

A summary of the main equations and formulae of the Brussels formalism (including the asymptotic theory, the ΩΨ-operator, the transformation theory and the redefined initial condition) is provided and discussed with the aid of formal techniques avoiding duplications of the proofs for homogeneous and inhomogeneous systems and stressing the mathematical structure. Applications to Lorentz transformations of the asymptotic master equations and to the formal collision operator are also discussed. This first part is devoted to the derivation of the exact master equations and a discussion of their basic properties.

Résumé. — Nous appliquons la théorie générale des processus irréversibles développée par I. Prigogine et collaborateurs au problème particulier du mouvement d'une particule lourde chargée (masse M) dans un fluide de bosons (masse m ; γ = (m / M)1/2 ⩽ 1) sous l'influence d'un champ électrique extérieur. Nous obtenons des résultats similaires à ceux obtenus récemment par P. Résibois et H. T. Davis dans le cas classique : à l'ordre le plus bas en γ, la particule brownienne obéit à une équation de Fokker-Planck classique mais avec un coefficient de friction quantique.
Comme application de cette méthode, nous évaluons explicitement la constante de friction d'un ion lourd immergé dans un fluide dilué de Bose ; le résultat obtenu est en accord satisfaisant avec les expériences de I. Meyer et F. Reif sur l'He4 liquide.

Les formes asymptotiques de l'équation cinétique générale, obtenue dans un article précédent [1] sont données. Pour un plasma faiblement stable ou instable les termes oscillants sont supprimés en utilisant une méthode proposée par Balescu [2]. Le lien entre la théorie cinétique et la théorie d'interaction particules-ondes est indiqué.