On the fractional perturbation theory and optical transitions in bulk semiconductors: Emergence of negative damping and variable charged mass

Abstract

This study is devoted to the construction of a fractional perturbation theory which represents the basic technique of approximation in quantum mechanics. Our analysis is based on the fractional actionlike variational approach (FALVA) implementation of fractionality. After discussing the basic properties of fractional harmonic oscillator through the fractional Feynman's path integral approach, we have discussed the Rabi oscillations within the context of two-level quantum systems for simulated optical transition. In particular the case α>1 is correlated to the emergence of negative damping and negative probabilities which have been obtained in several quantum out-of-equilibrium systems. The fractional Fermi Golden rule and the fractional Heisenberg's uncertainty principle have been also obtained and their main properties and features have been discussed accordingly. We have discussed optical transitions in bulk semiconductors. It was observed that the fundamental properties of transitions rates are recovered if the charged particle moving inside the semiconductor is variable with time.