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The phase-space formulation of the electron dynamics in the condensed matter is well established kinetic method describing transport phenomena in the systems [1]. Originally this method was based on the classical equations of statistical physics, and their applications depend on an actual physical situation. However, none of these equations is suitable for a description of the transport properties of nanoscale nanodevices in which the quantum phenomena play primary role. In some sense, the nanosystems can be regarded as a training ground for an observation these phenomena and testing a variety of concepts associated with them. To meet these expectations, the quantum generalisation of the kinetic method can be based on the density operator and its equation of motion in the mixed position-momentum representation proposed by Weyl and Wigner [2]. In this representation, the phase space acquires new properties which lead to a loss of the commutative property, and the dynamical variables defined over the space form the non-commutative algebra. This observation suggests that the position and momentum are mutually dependent variables. In this report we present results of our studies concerning the position-momentum correlations of the conduction electrons in a simple resonant-tunelling nanosystem. We investigate the influence of the scattering processes which destroys the phase coherence of the tunelling electrons through the double-barrier nanostructure on the considered correlations between these two dynamical variables. For this purpose, we solve the quantum kinetic equation for the Wigner distribution function (WDF) within the relaxation time approximation and determine the symmetrical correlation function of the first order as a function of the relaxation time for different points at the current–voltage characteristics.

acta physica polonica. a

Synthesis and Characterization of Gd2O2SO4:Pr3+ Scintillation Material Produced by Sol-Gel Process for Digital Imaging System