Extended class of phenomenological universalities

Abstract

The phenomenological universalities (PU) are extended to include quantum oscillatory phenomena, coherence and supersymmetry. It will be proved that this approach generates minimum uncertainty coherent states of time-dependent oscillators, which in the dissociation (classical) limit reduce to the functions describing growth (regression) of the systems evolving over time. The PU formalism can be applied also to construct the coherent states of space-dependent oscillators, which in the dissociation limit produce cumulative distribution functions widely used in probability theory and statistics. A combination of the PU and supersymmetry provides a convenient tool for generating analytical solutions of the Fokker–Planck equation with the drift term related to the different forms of potential energy function. The results obtained reveal existence of a new class of macroscopic quantum (or quasi-quantum) phenomena, which may play a vital role in coherent formation of the specific growth patterns in complex systems.