Bohm’s quantum-force time series: Stable distribution, flat power spectrum, and implication

New insight into the nature of Bohm’s quantum force is presented. Based on our numerical study, we conclude that, for the kicked pendulum, Bohm’s quantum-force time-series for nonstationary states is typically or generically non-Gaussian stable distributed with a flat power spectrum. For fixed system parameters and initial wave function, the stable parameters and the constant value of the power spectrum are independent of the initial Bohmian angle. We conjecture that these properties of the quantum-force time-series are also typical or generic for other classically chaotic Hamiltonian dynamical systems since the kicked pendulum is a prototypical member of this class of systems. A new method of calculating the quantum probability density of a particle’s position implied by these quantum-force properties is described.