EPJ D Topical Review - Applied Bohmian Mechanics

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Published on 29 September 2014

Bohmian mechanics provides an explanation of quantum phenomena in terms of point particles guided by wave functions. This EPJ D review focuses on the formalism of non-relativistic Bohmian mechanics, rather than its interpretation, and although the Bohmian and standard quantum mechanical theories have different formalisms, they both yield exactly the same predictions for all phenomena.

Fifteen years ago the quantum chemistry community began to study the practical utility of Bohmian mechanics, and since that time the scientific community has primarily applied it to the study of the (unitary) evolution of single-particle wave functions, either by developing efficient quantum trajectory algorithms or by providing a trajectory-based explanation of complicated quantum phenomena.

Here, the authors present a large list of examples showing how the Bohmian formalism provides a useful solution in different forefront research fields for problems where the Bohmian and quantum hydrodynamic formalisms coincide.

In addition, this work emphasises that the Bohmian formalism can be a useful tool in other types of (non-unitary and non-linear) quantum mechanical problems, where the influence of the environment on the global wave function is unknown. This review also contains examples illustrating the use of the Bohmian formalism for the many-body problem, decoherence and measurement processes. To date, the ability of the Bohmian formalism to analyse this last type of problem for (open) quantum systems remains largely unexplored by the scientific community. The authors of this review are convinced that the final status of the Bohmian theory amongst members of the scientific community will be greatly influenced by its potential to solve problems that present non-unitary and/or non-linear quantum evolutions. A brief introduction to the Bohmian formalism and some of its extensions are presented in the last part of this review.