Bohmian mechanics, the quantum-classical correspondence and the classical limit: the case of the square billiard

TL;DR

This paper compares quantum and classical dynamics in square billiards, analyzing wavepacket evolution, Bohmian trajectories, and the role of decoherence, highlighting non-classical features of Bohmian paths even in the classical limit.

Contribution

It provides a detailed analysis of Bohmian trajectories in quantum square billiards and discusses their divergence from classical paths, challenging decoherence as a solution for classicality.

Findings

Bohmian trajectories are generally non-classical and follow probability flow streamlines.

Wavepacket evolution aligns with classical orbits but Bohmian paths do not.

Decoherence does not necessarily lead to classical behavior in this system.

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.