Bohmian description of a decaying quantum system

Nogami, Y.; Toyama, F. M.; Dijk, W. van

doi:10.1016/s0375-9601(00)00328-5

Cited by 21 publications

(11 citation statements)

References 41 publications

(30 reference statements)

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“…It must be emphasized that backflow occurs for the potential barrier model and for the free particle case, but the interference causing it has different origins, viz., exponential and inverse-power law for the δ barrier, and two or more different exponential regions for the free particle. It would be interesting to investigate the free particle "decay" using Bohmian mechanics as we did for the δ barrier [10,21]. Initial work on this is promising.…”

Section: Summary and Concluding Commentsmentioning

confidence: 99%

Decay of a quasistable quantum system and quantum backflow

Dijk

Toyama

2019

Phys. Rev. A

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The decay of quasi-stable quantum system involves primarily an outgoing probability current density. However, during the transition from exponential to inverse-power-law decay there are time intervals during which this current, although small, is inward. In this paper this inward flow is associated with quantum backflow. Furthermore substantial backflow exists for time-evolving free wave packets which are initially confined in space.

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Section: Summary and Concluding Commentsmentioning

confidence: 99%

Decay of a quasistable quantum system and quantum backflow

Dijk

Toyama

2019

Phys. Rev. A

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“…We argue that one should study Eq. (14), where the variances at t = 0 in the right hand side of the expression are limited by the Heisenberg uncertainty in Eq. (11), to determine to which extent we can speak of possible angular alignment.…”

Section: Opposite Momenta and Opposite Directionsmentioning

confidence: 99%

“…Toyama and W. van Dijk [14], where a decaying system is represented by a particle that leaks out from a region surrounded by a repulsive potential barrier.…”

Section: Bohmian Picture Of a Decaying Systemmentioning

confidence: 99%

On Peres' Statement “Opposite Momenta Lead to Opposite Directions,” Decaying Systems and Optical Imaging

Struyve

Baere

Neve

et al. 2004

Foundations of Physics

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We re-examine Peres' statement "opposite momenta lead to opposite directions". It will be shown that Peres' statement is only valid in the large distance or large time limit. In the short distance or short time limit an additional deviation from perfect alignment occurs due to the uncertainty of the location of the source. This error contribution plays a major role in Popper's orginal experimental proposal. Peres' statement applies rather to the phenomenon of optical imaging, which was regarded by him as a verification of his statement. This is because this experiment can in a certain sense be seen as occurring in the large distance limit. We will also reconsider both experiments from the viewpoint of Bohmian mechanics. In Bohmian mechanics particles with exactly opposite momenta will move in opposite directions. In addition it will prove particularly usefull to use Bohmian mechanics because the Bohmian trajectories coincide with the conceptual trajectories drawn by Pittman et al. In this way Bohmian mechanics provides a theoretical basis for these conceptual trajectories.

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“…The de Broglie Bohm (BB) theory is by far the best-known and most developed of hidden-variables theories, and BB trajectories have been computed for a wide range of quantum systems (see [4] and Refs therein as well as more recent work e.g. [5,6,7,8]. One of the main motivations behind the BB theory is to bridge the gap between classical and quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Can Bohmian trajectories account for quantum recurrences having classical periodicities?

Matzkin

2007

Physics Letters A

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Quantum systems in specific regimes display recurrences at the period of the periodic orbits of the corresponding classical system. We investigate the excited hydrogen atom in a magnetic field -a prototypical system of 'quantum chaos' -from the point of view of the de Broglie Bohm (BB) interpretation of quantum mechanics. The trajectories predicted by BB theory are computed and contrasted with the time evolution of the wavefunction, which shows pronounced features at times matching the period of closed orbits of the classical hydrogen in a magnetic field problem.Individual BB trajectories do not possess these periodicities and cannot account for the quantum recurrences. These recurrences can however be explained by BB theory by considering the ensemble of trajectories compatible with an initial statistical distribution, although none of the trajectories of the ensemble are periodic, rendering unclear the dynamical origin of the classical periodicities.

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Bohmian description of a decaying quantum system

Cited by 21 publications

References 41 publications

Decay of a quasistable quantum system and quantum backflow

Decay of a quasistable quantum system and quantum backflow

On Peres' Statement “Opposite Momenta Lead to Opposite Directions,” Decaying Systems and Optical Imaging

Can Bohmian trajectories account for quantum recurrences having classical periodicities?

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