Dynamic Behavior of Kink-Solitons at Junctions in Quantum-Dot Cellular Automata

We examine the propagation of electric polarization in quantum-dot cellular automata (QCA) as a kink-soliton. Focusing on its behavior at a junction between different kinds of QCA, we solve the time-dependent Schrödinger equation numerically using the Hartree approximation and an exact method. Using the Hartree approximation, the soliton is perfectly transmitted or reflected, like a classical particle. This property agrees with the numerical solution of the nonlinear wave equation obtained in the continuum limit. The exact calculation method yields different behavior patterns for the solitons at the junction, partly transmitted and partly reflected, similar to a quantum wave packet.