Damian Kołaczek, Bartłomiej J. Spisak and Maciej Wołoszyn
Using the phase space approach, we consider the quantum dynamics of a wave packet in an isolated confined system with three different potential energy profiles. We solve the Moyal equation of motion for the Wigner function with the highly efficient spectral split-operator method. The main aim of this study is to compare the accuracy of the employed algorithm through analysis of the total energy expectation value, in terms of deviation from its exact value. This comparison is performed for the second and fourth order factorizations of the time evolution operator.
Karol Kulinowski, Maciej Wołoszyn, Marta Radecka and Bartłomiej J. Spisak
The purpose of this study is to apply the distribution function formalism to the problem of electronic transport in open systems, and to numerically solve the kinetic equation with a dissipation term. This term is modeled within the relaxation time approximation and contains two parts, corresponding to elastic or inelastic processes. The collision operator is approximated as a sum of the semi-classical energy dissipation term and the momentum relaxation term, which randomizes the momentum but does not change the energy. As a result, the distribution of charge carriers changes due to the dissipation processes, which has a profound impact on the electronic transport through the simulated region discussed in terms of the current–voltage characteristics and their modification caused by the scattering. Measurements of the current–voltage characteristics for titanium dioxide thin layers are also presented, and compared with the results of numerical calculations.