Weak measurements of trajectories in quantum systems: classical, Bohmian and sum over paths

TL;DR

This paper investigates how weak measurements can reveal quantum trajectories, comparing classical, Bohmian, and path integral approaches using a time-dependent oscillator model.

Contribution

It provides a comparative analysis of trajectory definitions from weak measurements, connecting them to Feynman propagators and Bohmian mechanics.

Findings

Weak measurements can approximate quantum trajectories.

Different approaches yield consistent insights into quantum dynamics.

The oscillator model illustrates the relation between weak values and underlying trajectories.

Abstract

Weak values, obtained from weak measurements, attempt to describe the properties of a quantum system as it evolves from an initial to a final state, without practically altering this evolution. Trajectories can be defined from weak measurements of the position, or inferred from weak values of the momentum operator. The former can be connected to the asymptotic form of the Feynman propagator and the latter to Bohmian trajectories. Employing a time-dependent oscillator as a model, this work analyzes to what extent weak measurements can shed light on the underlying dynamics of a quantum system expressed in terms of trajectories, in particular by comparing the two approaches.