Characteristic times for thermal wave packets in dissipative Bohmian mechanics: the parabolic repeller

TL;DR

This paper investigates how thermal wave packets behave in dissipative Bohmian mechanics when passing through a parabolic repeller, focusing on characteristic times and transmission probabilities at various temperatures.

Contribution

It introduces a detailed analysis of thermal wave packet dynamics in dissipative Bohmian mechanics, incorporating both linear and nonlinear dissipation models with temperature effects.

Findings

Dissipation affects transmission and reflection times significantly.

Thermal effects enable non-tunneling transmission at nonzero temperatures.

Characteristic times depend on initial conditions and dissipation models.

Abstract

Thermal wave packets are used to analyze transmission probabilities and characteristic times through a parabolic repeller within the dissipative Bohmian mechanics. Thermal arrival, dwelling, transmission and reflection times are defined and calculated by using a Maxwell-Boltzmann distribution for the initial velocities of the incident particles. The dissipation is considered within the Caldirola-Kanai and Kostin approaches where a linear and nonlinear framework is used, respectively. The initial parameters are chosen to have only a dissipative tunnelling dynamics at zero temperature; at any nonzero temperature, transmission proceeds not only via tunnelling.