Bohmian Trajectories Post-Decoherence

TL;DR

This paper investigates how Bohmian trajectories become approximately classical after decoherence, especially when the system starts in an energy eigenstate, and explores the connection with environmental information storage.

Contribution

It demonstrates that Bohmian trajectories tend to become classical post-decoherence under specific initial conditions, linking this to environmental monitoring and the behavior of the Wigner function.

Findings

Bohmian trajectories approximate classical paths after decoherence.

Initial energy eigenstates facilitate classical behavior emergence.

Environmental information storage influences trajectory classicality.

Abstract

The proposal that the interaction between a macroscopic body and its environment plays a crucial role in producing the correct classical limit in the Bohm interpretation of quantum mechanics is investigated, in the context of a model of quantum Brownian motion. It is well known that one of the effects of the interaction is to produce an extremely rapid approximate diagonalisation of the reduced density matrix in the position representation. This effect is, by itself, insufficient to produce generically quasi-classical behaviour of the Bohmian trajectory. However, it is shown that, if the system particle is initially in an approximate energy eigenstate, then there is a tendency for the Bohmian trajectory to become approximately classical on a rather longer time-scale. The relationship between this phenomenon and the behaviour of the Wigner function post-decoherence (as analysed by Halliwell and Zoupas) is discussed. It is also suggested that the phenomenon may be related to the storage of information about the trajectory in the environment, and that it may therefore be a general feature of every situation in which such environmental monitoring occurs.