Bohmian Classical Limit in Bounded Regions

TL;DR

This paper investigates how classical trajectories emerge from Bohmian mechanics within bounded regions, proposing that environmental decoherence with stronger conditions can facilitate the classical limit.

Contribution

It identifies the need for disjoint support conditions, beyond orthogonality, to effectively implement decoherence in Bohmian systems in bounded regions.

Findings

Disjoint support condition is necessary for decoherence in Bohmian mechanics.

Classical trajectories can emerge through environmental decoherence under stronger support conditions.

The paper addresses technical challenges of Bohmian dynamics in bounded regions.

Abstract

Bohmian mechanics is a realistic interpretation of quantum theory. It shares the same ontology of classical mechanics: particles following continuous trajectories in space through time. For this ontological continuity, it seems to be a good candidate for recovering the classical limit of quantum theory. Indeed, in a Bohmian framework, the issue of the classical limit reduces to showing how classical trajectories can emerge from Bohmian ones, under specific classicality assumptions. In this paper, we shall focus on a technical problem that arises from the dynamics of a Bohmian system in bounded regions; and we suggest that a possible solution is supplied by the action of environmental decoherence. However, we shall show that, in order to implement decoherence in a Bohmian framework, a stronger condition is required (disjointness of supports) rather than the usual one (orthogonality of states).