Transmission time and resonant tunneling through barriers using localized quantum density soliton waves

Abstract

In this paper, the interaction and transmission time of quantum density solitons waves [B. M. Mirza, Mod. Phys. Lett. B 28 (2014) 1450200]1 passing through finite barrier potentials is investigated. Using the conservation of energy and of quantum density, it is first demonstrated that the soliton waves possess the important particle-like properties, including localization by a finite de Broglie wavelength and constant uniform motion in free space. The passage of quantum density solitons through barriers of finite energies is then shown to lead to the phenomena of resonant tunneling and, in Josephson-like configurations, to the quantization of magnetic flux. A precise general measure for barrier tunneling time is derived which is found to give a new interpretation of the quantum indeterminacy principles. The quantum density soliton theory is applied to coherent microstructures observed in NbSe 3-like systems, where it is shown to lead to the sawtooth current phenomena and nano-scale transversal times.