Kink-solitons in quantum-dot cellular automata

We examine the propagation of electric polarization in quantum-dot cellular automata (QCA) as a kink-soliton. We solve the time-dependent Schrödinger equation numerically by the Hartree approximation and also by the exact method. By the Hartree approximation, we find that the shape of the kink-soliton can be fitted very well to a function of hyperbolic tangent, which coincides with the solution of the nonlinear wave equation obtained in the continuum limit. At the junction between different kinds of QCA, the soliton is perfectly transmitted or reflected, like a classical particle. The exact calculations yield different behaviors of kink-solitons at the junction; partly transmitted and partly reflected, similar to a quantum wave packet.