Bohmian Mechanics, Open Quantum Systems and Continuous Measurements by Antonio B. Nassar & Salvador Miret-Artés

Author:Antonio B. Nassar & Salvador Miret-Artés
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(2.269)

With , the transition from a uniformly accelerated motion, displayed by the wave-packet centroid, to a uniform rectilinear one, as a consequence of the damping, becomes more apparent. The expression for the average energy is given by

(2.270)

In the limit , this expression approaches

(2.271)

Unlike the example of the free wave packet, here the energy does not approach zero asymptotically, but it continues decreasing below it as the wave packet slides downhill (unless some additional constraint is imposed in the dynamics to avoiding this situation). Nevertheless, although there is no suppression of the motion, spatial localization is still present.

On the other hand, due to the fact that does not depend on the potential function, the functional form displayed by the Bohmian trajectories is exactly the same as in the free case, except for the fact that these trajectories contain information about the acceleration undergone by the centroid (this information is transmitted through ). Now, once the exponentials have vanished, all these trajectories evolve parallel one another, just like classical trajectories under similar circumstances.

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