Applied Bohmian mechanics

TitleApplied Bohmian mechanics
Publication TypeJournal Article
Year of Publication2014
AuthorsBenseny, A, Albareda, G, Sanz, AS, Mompart, J, Oriols, X
JournalEuropean Physical Journal D
Start Page286
Date Published10/2014
Type of ArticleTopical Review

Bohmian mechanics provides an explanation of quantum phenomena in terms of point-like particles
guided by wave functions. This review focuses on the use of nonrelativistic Bohmian mechanics to
address practical problems, rather than on its interpretation. Although the Bohmian and standard quantum
theories have different formalisms, both give exactly the same predictions for all phenomena. Fifteen years
ago, the quantum chemistry community began to study the practical usefulness of Bohmian mechanics.
Since then, the scientific community has mainly applied it to study the (unitary) evolution of single-particle
wave functions, either by developing efficient quantum trajectory algorithms or by providing a trajectorybased
explanation of complicated quantum phenomena. Here we present a large list of examples showing
how the Bohmian formalism provides a useful solution in different forefront research fields for this kind
of problems (where the Bohmian and the quantum hydrodynamic formalisms coincide). In addition, this
work also emphasizes that the Bohmian formalism can be a useful tool in other types of (nonunitary
and nonlinear) quantum problems where the influence of the environment or the nonsimulated degrees of
freedom are relevant. This review contains also examples on the use of the Bohmian formalism for the
many-body problem, decoherence and measurement processes. The ability of the Bohmian formalism to
analyze this last type of problems for (open) quantum systems remains mainly unexplored by the scientific
community. The authors of this review are convinced that the final status of the Bohmian theory among
the scientific community will be greatly influenced by its potential success in those types of problems that
present nonunitary and/or nonlinear quantum evolutions. A brief introduction of the Bohmian formalism
and some of its extensions are presented in the last part of this review.

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