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

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.Comment: Figures downgraded to low resolution; To be published in Found. Phys. (2009)

Calbindin D-28k and parvalbumin immunoreactivity in the frontal cortex in patients with frontal lobe dementia of non-Alzheimer type associated with amyotrophic lateral sclerosis.

The morphology and distribution of local-circuit neurons (interneurons) were examined, by calbindin D-28k and parvalbumin immunocytochemistry, in the frontal cortex (area 8) in two patients with frontal lobe dementia of non-Alzheimer type associated with classical amyotrophic lateral sclerosis (ALS), and in seven normal cases. The density of calbindin D-28k immunoreactive cells was dramatically reduced in ALS patients, but the density of parvalbumin-immunoreactive neurons was preserved. Decreased density of calbindin D-28k-immunoreactive neurons, which are mainly located in the upper cortical layers, may interfere with the normal processing of cortico-cortical connections, whereas integrity of parvalbumin-immunoreactive cells may be associated with the preservation of the major inhibitory intracortical circuits in patients with frontal lobe dementia