Partial integrability of 3d Bohmian trajectories

In this paper we study the integrability of 3d Bohmian trajectories of a system of quantum harmonic oscillators. We show that the initial choice of quantum numbers is responsible for the existence (or not) of an integral of motion which confines the trajectories on certain invariant surfaces. We giv...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 50; no. 19; pp. 195101 - 195113
Main Authors Contopoulos, G, Tzemos, A C, Efthymiopoulos, C
Format Journal Article
LanguageEnglish
Published IOP Publishing 12.05.2017
Subjects
Bohmian quantum mechanics
nonlinear dynamics
quantum chaos
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Summary:In this paper we study the integrability of 3d Bohmian trajectories of a system of quantum harmonic oscillators. We show that the initial choice of quantum numbers is responsible for the existence (or not) of an integral of motion which confines the trajectories on certain invariant surfaces. We give a few examples of orbits in cases where there is or there is not an integral and make some comments on the impact of partial integrability in Bohmian Mechanics. Finally, we make a connection between our present results for the integrability in the 3d case and analogous results found in the 2d and 4d cases.
Bibliography:JPhysA-107012.R1
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aa685d