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Square billiards are quantum systems complying with the dynamicalquantum-classical correspondence. Hence an initially localized wavefunctionlaunched along a classical periodic orbit evolves along that orbit, thespreading of the quantum amplitude being controlled by the spread of thecorresponding classical statistical distribution. We investigate wavepacketdynamics and compute the corresponding de Broglie-Bohm trajectories in thequantum square billiard. We also determine the trajectories and statisticaldistribution dynamics for the equivalent classical billiard. Individual Bohmiantrajectories follow the streamlines of the probability flow and are genericallynon-classical. This can also hold even for short times, when the wavepacket isstill localized along a classical trajectory. This generic feature of Bohmiantrajectories is expected to hold in the classical limit. We further argue thatin this context decoherence cannot constitute a viable solution in order torecover classicality.

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