Numerical validation of Ehrenfest theorem in a Bohmian perspective for non-conservative systems

TL;DR

This paper conducts a high-precision numerical validation of Ehrenfest's theorem within the Bohmian framework, analyzing quantum and classical dynamics for harmonic and Duffing oscillators under various external forces.

Contribution

It provides a detailed numerical analysis of Ehrenfest's theorem in Bohmian mechanics for non-conservative systems, including external force effects and resonance phenomena.

Findings

Quantum trajectories align with classical solutions under certain conditions.

External forces influence the quantum-classical correspondence, with resonance observed.

Bohmian averages effectively reproduce classical dynamics in the studied systems.

Abstract

In this work we make a high precision numerical study of the Ehrenfest theorem using the Bohmian approach, where we obtain classical solutions from the quantum trajectories performing the Bohmian averages. We analyse the one-dimensional quantum harmonic and Duffing oscillator cases, finding numerical solutions of the time-dependent Schr\"odinger equation and the guidance equation for different sets of initial conditions and connects these results with the corresponding classical solutions. We also investigate the effect of introducing external forces of three types: a simple constant force, a fast-acting Gaussian impulse, and an oscillatory force with different frequencies. In the last case the resonance in the quantum trajectories was observed.