Our previous results [V.N. Kuzovkov, W. von Niessen, V. Kashcheyevs, O. Hein, J. Phys. Condens. Matter 14 (2002) 13777] dealing with the analytical solution of the two-dimensional (2-D) Anderson localization problem due to disorder is generalized for anisotropic systems (two different hopping...

In the realm of Ehrenfest’s theorem, classical trajectories obeying Newton’s laws have been proven useful to construct explicit solutions to the time-dependent Wigner–Liouville equation. Whereas previous works have particularly focused on the initial distribution function as a vehicle...

The capability of manipulating single dopant atoms in semiconductor materials, with atomic precision, has given birth to a new branch of electronics known as solotronics (solitary dopant optoelectronics). While experiments are advancing rapidly, the theoretical comprehension of quantum phenomena...

A type of non-Hermitian generalization of quantum mechanics is discussed. We introduce an imaginary vector potential to the Hamiltonian of systems such as Anderson-localization systems and mesoscopic systems. In these systems the imaginary part of the wave number of the eigenfunction asymptote...

The motion of carriers in an external field is modelled by Monte Carlo simulation in two-dimensional continuous space. The mean square displacement 〈R2〉 of carriers as functions of the relative field strength λ and time t is carried out by theoretical calculation and numerical simulation....

We discuss here in detail a new analytical random walk approach to calculating the phase diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from delocalized to localized states is treated as a generalized...