Atom-diffraction from surfaces with defects: A Fermatian, Newtonian and Bohmian joint view

TL;DR

This paper compares quantum, Fermatian, Newtonian, and Bohmian approaches to helium atom diffraction on defective surfaces, revealing how classical and quantum features relate and differ in trajectory-based models.

Contribution

It provides a comparative analysis of multiple trajectory-based models, including Bohmian mechanics, in describing atom-surface diffraction with defects.

Findings

Bohmian trajectories differ significantly from classical trajectories.

Fermatian and Newtonian trajectories show some similarities.

Quantum diffraction patterns are better understood through trajectory analysis.

Abstract

Bohmian mechanics, widely known within the field of the quantum foundations, has been a quite useful resource for computational and interpretive purposes in a wide variety of practical problems. Here, it is used to establish a comparative analysis at different levels of approximation in the problem of the diffraction of helium atoms from a substrate consisting of a defect with axial symmetry on top of a flat surface. The motivation behind this work is to determine which aspects of one level survive in the next level of refinement and, therefore, to get a better idea of what we usually denote as quantum-classical correspondence. To this end, first a quantum treatment of the problem is performed with both an approximated hard-wall model and then with a realistic interaction potential model. The interpretation and explanation of the features displayed by the corresponding diffraction intensity patterns is then revisited with a series of trajectory-based approaches: Fermatian trajectories (optical rays), Newtonian trajectories and Bohmian trajectories. As it is seen, while Fermatian and Newtonian trajectories show some similarities, Bohmian trajectories behave quite differently due to their implicit non-classicality.