The scattered wave formalism developed for a quantum subsystem interacting with reservoirs through open boundaries is applied to one- or two-dimensional barrier scattering and quantum transistors. The total wave function is divided into incident and scattered components. Markovian outgoing wave boundary conditions are imposed on the scattered or total wave function by either the ratio or polynomial methods. For barrier scattering problems, accurate time-dependent transmission probabilities are obtained through the integration of the modified time-dependent Schrödinger equations for the scattered wave function. For quantum transistors, the time-dependent transport is studied for a quantum wave packet propagating through the conduction channel of a field effect transistor. This study shows that the scattered wave formalism significantly reduces computational effort relative to other open boundary methods and demonstrates wide applications to quantum dynamical processes.

• Received 9 June 2011

DOI:https://doi.org/10.1103/PhysRevE.84.056707