Diffraction and interference of matter waves are key phenomena
in quantum mechanics. Here we present some results on particle
diffraction in a wide variety of situations, ranging from simple
slit experiments to more complicated cases such as atom
scattering by corrugated metal surfaces and metal surfaces with
simple and isolated adsorbates. The principal novelty of our
study is the use of the so-called Bohmian formalism of quantum
trajectories. These trajectories are able to satisfactorily
reproduce the main features of the experimental results and,
more importantly, they provide a causal intuitive interpretation
of the underlying dynamics. In particular, we will focus our
attention on: (a) a revision of the concepts of near and far
field in undulatory optics; (b) the transition to the classical
limit, where it is found that although the quantum and classical
diffraction patterns tend to be quite similar, some quantum
features are maintained even when the quantum potential goes to
zero; and (c) a qualitative description of the scattering of
atoms by metal surfaces in the presence of a single adsorbate.
The method of quantum trajectories proposed by de Broglie and Bohm is applied to the study of atom diffraction by surfaces. As an example, a realistic model for the scattering of He off corrugated Cu is considered. In this way, the final angular distribution of trajectories is obtained by box counting, which is in excellent agreement with the results calculated by standard S matrix methods of scattering theory. More interestingly, the accumulation of quantum trajectories at the different diffraction peaks is explained in terms of the corresponding quantum potential. This nonlocal potential ''guides'' the trajectories causing a transition from a distribution near the surface, which reproduces its shape, to the final diffraction pattern observed in the asymptotic region, far from the diffracting object. These two regimes are homologous to the Fresnel and Fraunhofer regions described in undulatory optics. Finally, the turning points of the quantum trajectories provide a better description of the surface electronic density than the corresponding classical ones, usually employed for this task.
In this work, a full quantum study of the scattering of He atoms off single CO molecules, adsorbed onto the Pt(111) surface, is presented within the formalism of quantum trajectories provided by Bohmian mechanics. By means of this theory, it is shown that the underlying dynamics is strongly dominated by the existence of a transient vortitial trapping with measurable effects on the whole diffraction pattern. This kind of trapping emphasizes the key role played by quantum vortices in this scattering. Moreover, an analysis of the surface rainbow effect caused by the local corrugation that the CO molecule induces on the surface, and its manifestation in the corresponding intensity pattern, is also presented and discussed.
The effects of incoherence and decoherence in the double--slit experiment are
studied using both optical and quantum--phenomenological models. The results
are compared with experimental data obtained with cold neutrons.Comment: 8 pages, 3 figure
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