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Physics Letters A

Chaotic Bohm's trajectories in a quantum circular billiard

O. F. de Alcantara Bonfim, J. Florencio, F. C. Sá Barreto

Published Nov 1, 2000• 9 citations
Publisher
DOI
10.1016/s0375-9601(00)00705-2

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The dynamics of a particle in square and circular billiards is studied within the framework of Bohm's quantum mechanics. While conventional quantum mechanics predicts that the system shows no indication of chaotic behavior for these geometries from either the eigenvalue spectra distribution or the structure of the eigenfunctions, we find that in Bohm's quantum mechanics these systems exhibit both regular and chaotic behavior, depending on the form of the initial wave packet and on the particle's initial position.
Right triangular billiards are very simple systems that are completely integrable in classical mechanics for acute angle pairs (45 degrees,45 degrees ) and (30 degrees,60 degrees ). In quantum mechanics, the energy level spacing distribution of these billiards are neither Poisson-like nor Wigner-like. We use Bohm's formalism to calculate the trajectories, by numerical methods, for a particle inside these billiards. We use a linear combination of the first three energy states as the initial wave function. We show that a particle can have quasiperiodic or chaotic behavior, depending on its initial position in the billiards.