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Foundations of Physics

, Volume 39, Issue 8, pp 903–920 | Cite as

Bohmian Mechanics, the Quantum-Classical Correspondence and the Classical Limit: The Case of the Square Billiard

  • A. Matzkin
Article

Abstract

Square billiards are quantum systems complying with the dynamical quantum-classical correspondence. Hence an initially localized wavefunction launched along a classical periodic orbit evolves along that orbit, the spreading of the quantum amplitude being controlled by the spread of the corresponding classical statistical distribution. We investigate wavepacket dynamics and compute the corresponding de Broglie-Bohm trajectories in the quantum square billiard. We also determine the trajectories and statistical distribution dynamics for the equivalent classical billiard. Individual Bohmian trajectories follow the streamlines of the probability flow and are generically non-classical. This can also hold even for short times, when the wavepacket is still localized along a classical trajectory. This generic feature of Bohmian trajectories is expected to hold in the classical limit. We further argue that in this context decoherence cannot constitute a viable solution in order to recover classicality.

Keywords

Quantum-classical correspondence Bohmian mechanics Classical limit Square billiard 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Laboratoire de Spectrométrie Physique (CNRS Unité 5588)Université Joseph-Fourier Grenoble-1Saint-Martin d’HèresFrance

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