In this paper I present new results about the complete quantum-relativistic form of the mean square deviation of position R2 (t) related to a recently appeared Drude-Lorentz-like model already performed at classical, quantum and relativistic level, named DS model. The function R2 (t) gives precise information about the distance traveled by a carrier (electrons, ions, etc.) inside a nanostructure, in the hypothesis of both quantum effects and relativistic velocities. The model has a wide scale range of applicability; the nanoscale is considered in this paper, but the model holds from sub-pico-level to macro-level because of the presence of a gauge factor, making it applicable to all oscillating processes in Nature. Examples of application and suggestions complete the paper.