Ahmed Al-Jamel, Dynamics of heavy quarkonia in memory-dependent dissipative environment from Bohmian trajectory perspective, International Journal of Modern Physics AVol. 33, No. 28, 1850164 (2018) .
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 $\tau$ and non-singular kernel $K(x,t)$ of two parameters $a,b$. By assuming a Gaussian packet wavefunction, we derived a MDD-Langevin equation (MDDLE). The general behavioral solution $x_c(t)$ of the MDDLE is investigated for the case of Gaussian fluctuation force. Based on the miscellaneous choices of $a,b,\tau$, the findings is that $x_c(t)$ can exhibit distinct behaviors, such as monotonic and non-monotonic 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 $\omega$, the position correlation function $C_x(t)$ is then obtained and analyzed numerically. The analysis shows that this correlation function is also sensitive to the various choices of $\tau$ 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 memorydependent experimental findings. The results are compared with the fractional Langevin equation.
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