Decoherence is defined as the emergence of classical properties through interaction with the environment. It is the most widely accepted concept to show how quantum systems become classical. In this view interference of the coherent superposition of quantum amplitudes R in Young's double slit experiment is a fundamental behavior of quantum systems, which leads to classical behavior, when interference vanishes, but quantum dispersion still holds. In the trajectory approach classical behavior means that the particles coming from one slit are not affected by the (empty) wave coming from the other slit and that the Bohm trajectories are able to cross the axis of symmetry.

In this video it is shown that decoherence is a sufficient mechanism, when a vector state wave function is assumed, to obtain the classical limit, which is in contrast to the general Bohmian view, where trajectories are not able to cross each other at the same time.
Further it is shown that the trajectories, calculated by de Broglie’s - and by Bohm's approach are different. But keep in mind that the vector state wave function is NOT standard Bohmian mechanics.
In de Broglie’s original approach, the particle dynamics is given by a first - order differential equation, which for short is called first order approach (FOA). In Bohm’s approach, Newton’s law of motion is completed with an extra potential, which is called quantum potential (QP). This method is called second order approach (SOA). In most of the cases and due to the initial positions and initial velocities both approaches are identical.
In the video on the left you see the trajectories (red) from the FOA. On the right you see the trajectories (White/blue) from the SOA.
An introduction to the Bohm de Broglie theory with Mathematica could be found:
[ Ссылка ]

Programmed by Klaus von Bloh

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