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Chaos in Bohmian Quantum Mechanics: A Short Review

Chaos in Bohmian Quantum Mechanics: A Short Review This is a short review of the theory of chaos in Bohmian quantummechanics based on our series of works in this field.Our first result is the development of a generic theoretical mechanismresponsible for the generation of chaos in anarbitrary Bohmian system (in 2 and 3 dimensions). This mechanismallows us to explore the effect of chaos on Bohmian trajectoriesand study in detail (both analytically and numerically) the different kinds of Bohmian trajectories where, in general,chaos and order coexist. Finally, we explore the effect of quantumentanglement on the evolution of the Bohmian trajectories and study chaos and ergodicity in qubit systems which are of great theoretical andpractical interest. We find that the chaotic trajectories are also ergodic, i. e., they give the same final distribution of their points after a long time regardless of their initial conditions. In the case of strong entanglement most trajectories are chaotic and ergodic and an arbitrary initial distribution of particles will tend to Born’s rule over the course of time. On the other hand, in the case of weak entanglement the distribution of Born’s rule is dominated by ordered trajectories and consequently an arbitrary initial configuration of particles will not tend, in general, to Born’s rule unless it is initially satisfied. Our results shed light on a fundamental problem in Bohmian mechanics, namely, whether there is a dynamical approximation of Born’s rule by an arbitrary initial distribution of Bohmian particles. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Chaos in Bohmian Quantum Mechanics: A Short Review

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References (69)

Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2020
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354720050056
Publisher site
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Abstract

This is a short review of the theory of chaos in Bohmian quantummechanics based on our series of works in this field.Our first result is the development of a generic theoretical mechanismresponsible for the generation of chaos in anarbitrary Bohmian system (in 2 and 3 dimensions). This mechanismallows us to explore the effect of chaos on Bohmian trajectoriesand study in detail (both analytically and numerically) the different kinds of Bohmian trajectories where, in general,chaos and order coexist. Finally, we explore the effect of quantumentanglement on the evolution of the Bohmian trajectories and study chaos and ergodicity in qubit systems which are of great theoretical andpractical interest. We find that the chaotic trajectories are also ergodic, i. e., they give the same final distribution of their points after a long time regardless of their initial conditions. In the case of strong entanglement most trajectories are chaotic and ergodic and an arbitrary initial distribution of particles will tend to Born’s rule over the course of time. On the other hand, in the case of weak entanglement the distribution of Born’s rule is dominated by ordered trajectories and consequently an arbitrary initial configuration of particles will not tend, in general, to Born’s rule unless it is initially satisfied. Our results shed light on a fundamental problem in Bohmian mechanics, namely, whether there is a dynamical approximation of Born’s rule by an arbitrary initial distribution of Bohmian particles.

Journal

Regular and Chaotic Dynamics – Springer Journals

Published: Sep 28, 2020

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