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.
Highlights
In the last several decades, there has been a fruitful and beneficial transfer of the ideas involved inDavid Bohm’s formulation of quantum mechanics [1,2,3,4] from the domain of the quantum foundations to the arena of the applications [5,6,7,8,9]
Rainbow features arise as a consequence of the local changes in the curvature of the interaction potential model [27,35], which give rise to accumulations of classical trajectories along some privileged directions, but that quantum-mechanically leave some uncertainties when we look at the corresponding diffraction patterns [29,32]
From which the probability |S(k i,x, k d,x )|2 is obtained to detect atoms that have exchanged a given amount ∆K of parallel momentum is obtained. This calculation is typically performed within a single unit cell; here, because of the lack of periodicity, the calculation involves an artificial cell of about 53 Å, which covers a region large enough as to include both the adsorbate and a good portion of the flat surface that is not influenced by artifacts related to the adsorbate curvature—this is appropriate to capture isolated signatures of trapping
Summary
In the last several decades, there has been a fruitful and beneficial transfer of the ideas involved in. The Newtonian level, where the He-CO/Pt(111) interaction is modeled in terms of a potential energy surface that smoothly changes from point to point This model has a repulsive wall that avoids He atoms to approach the substrate beyond a certain distance (for a given incidence energy), and an attractive tail that accounts for van der Waals long-range attraction. Rainbow features arise as a consequence of the local changes in the curvature of the interaction potential model [27,35], which give rise to accumulations of classical trajectories along some privileged directions (rainbow deflection angles), but that quantum-mechanically leave some uncertainties when we look at the corresponding diffraction patterns [29,32].
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