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 trajectory-based 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.

/pdf/applied-bohmian-mechanics-1n29klpepr.pdf

Applied Bohmian mechanics

http://digital.csic.es/bitstream/10261/130506/1/ALuis.pdf

What dynamics can be expected for mixed states in two-slit experiments?

We show how energy flow lines answer the question about diffraction phenomena posed in 1818 by the French Academy: “Deduce by mathematical induction the movements of the rays during their crossing near the bodies.” The use of energy flow lines provides a complementary answer to Fresnel’s wave theory of light. A numerical simulation of the energy flow lines shows that they can reach the bright spot of Poisson–Arago in the shadow center of a circular opaque disk. For a monochromatic wave in vacuum, these energy flow lines correspond to the diffracted rays of Newton’s Opticks.

Energy flow lines and the spot of Poisson–Arago

Weak-measurement-based experiments [Kocsis et al., Science 332 (2011) 1170] have shown that, at least for pure states, the average evolution of independent photons in Young's two-slit experiment is in compliance with the trajectories prescribed by the Bohmian formulation of quantum mechanics. But, what happens if the same experiment is repeated assuming that the wave function associated with each particle is different, i.e., in the case of mixed (incoherent) states? This question is investigated here by means of two alternative numerical simulations of Young's experiment, purposely devised to be easily implemented and tested in the laboratory. Contrary to what could be expected a priori, it is found that even for conditions of maximal mixedness or incoherence (total lack of interference fringes), experimental data will render a puzzling and challenging outcome: the average particle trajectories will still display features analogous to those for pure states, i.e., independently of how mixedness arises, the associated dynamics is influenced by both slits at the same time. Physically this simply means that weak measurements are not able to discriminate how mixedness arises in the experiment, since they only provide information about the averaged system dynamics.

/pdf/what-dynamics-can-be-expected-for-mixed-states-in-two-slit-4mb9v6amdb.pdf

To understand the processes behind seeing light, we need to integrate knowledge about the incoming optical structure, its perception, and how light interacts with material, shape, and space-objectively and subjectively. To that end, we need a novel approach to the science of light, namely, a transdisciplinary science of appearance, integrating optical, perceptual, and design knowledge and methods. In this article, I review existing literature as a basis for such a synthesis, which should discuss light in its full complexity, including its spatial properties and interactions with materials, shape, and space. I propose to investigate this by representing the endless variety of light, materials, shapes, and space as canonical modes and their combinations.

Light: Toward a Transdisciplinary Science of Appearance and Atmosphere.

Pictures of the energy density and the energy flow in distributions of incoherent light for various two-dimensional situations are shown and discussed. Rules are introduced that allow one to sketch and to interpret such pictures.

Which way does the light go

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Which way does the light go