Superquantum effects on physical systems from a hydrodynamic perspective

Abstract

Employing a nonlinear time-dependent Schrödinger equation that describes the transition between quantum and classical regimes, we explore superquantum effects on physical systems from a hydrodynamic point of view. The degree of quantumness, a pivotal parameter in this transition equation, gauges the impact of quantum effects arising from the quantum potential. As this parameter varies continuously between zero and one, it facilitates the gradual transformation of systems from purely classical to entirely quantum regimes. We extend our analysis by setting the degree of quantumness greater than one, thereby investigating superquantum phenomena. Notably, this transition equation can be reframed as a scaled time-dependent Schrödinger equation with a rescaled Planck constant. Through computational simulations derived from the scaled Schrödinger equation, we examine superquantum implications for two systems, including Gaussian wave packet scattering from an Eckart barrier and metastable state decay. This research suggests that the hydrodynamic formulation of the quantum–classical transition equation offers a profound understanding of superquantum influences on physical systems.