Z. Naturfors. Sect. A-J. Phys. Sci.

In this paper, we consider the dynamics of Klein-Gordon and Dirac oscillators in (2 + 1) dimensions with noncommutativity of the spatial coordinates using the supersymmetric path integral formalism. The propagator is calculated and the energy eigenvalues with their corresponding eigenfunctions are deduced

Фаза Берри для нестационарных связанных гармонических осцилляторов в некоммутативном фазовом пространстве с помощью методов интеграла по траектории

The purpose of this paper is the description of Berry’s phase, in the Euclidean Path Integral formalism, for 2D quadratic system: two time dependent coupled harmonic oscillators. This treatment is achieved by using the adiabatic approximation in the commutative and noncommutative phase spaceЦелью данной работы является описание фазы Берри в формализме евклидова интеграла по путям для двумерной квадратичной системы: двух связанных во времени гармонических осцилляторов. Эта обработка достигается с помощью адиабатического приближения в коммутативном и некоммутативном фазовом пространств

Numerical Approximation of Second-Order Elliptic Problems in Unbounded Domains

This paper deals with the numerical resolution of elliptic problems in unbounded domains using inverted finite elements. In opposition to conventional approaches which are based on the truncation of the domain, the suggested method keeps the domain unbounded and is based on a description of the asymptotic behavior in an appropriate functional framework. The method and its mathematical properties are presented first, and some computational examples are carried out. The obtained numerical results demonstrate the efficiency of the method