Dynamics of heavy quarkonia in memory-dependent dissipative environment from Bohmian trajectory perspective

Abstract

In this work, we study the dynamics of particles coupled to a dissipative environment from Bohmian trajectory perspective. The dissipation is modeled using the concept of memory-dependent derivative (MDD), which is characterized by its time-delay constant [Formula: see text] and nonsingular kernel [Formula: see text] of two parameters [Formula: see text], [Formula: see text]. By assuming a Gaussian packet wave function, we derived a MDD-Langevin equation (MDDLE). The general behavioral solution [Formula: see text] of the MDDLE is investigated for the case of Gaussian fluctuation force. Based on the miscellaneous choices of [Formula: see text], [Formula: see text], [Formula: see text], the findings are that [Formula: see text] can exhibit distinct behaviors, such as monotonic and nonmonotonic decay without zero crossings, oscillatory-like without zero and with zero crossing. Therefore, we have either diffusion or oscillatory dominate based on the problem parameters. For a harmonically bound heavy quarkonium, characterized by the angular frequency [Formula: see text], the position correlation function [Formula: see text] is then obtained and analyzed numerically. The analysis shows that this correlation function is also sensitive to the various choices of [Formula: see text] and kernel parameters. Based on these choices, the correlation function exhibits distinct behaviors: oscillation without damping, damping, and enhanced. This wide range of behavior coverage increases the versatility to fit nonlinear or memory-dependent experimental findings. The results are compared with the fractional Langevin equation.