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

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.

v2:minor changes (typos corrected, some points clarified, extended bibliography). Similar to the published version

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Cited by in corpus (5)

• Probing finite coarse-grained virtual Feynman histories with sequential weak values
• Single particle nonlocality, geometric phases and time-dependent boundary conditions
• Proposal to observe paths superpositions in a double-slit setup
• A New Quantum Operator for Distance
• Harmonizing de Broglie-Bohm's Causal Interpretation with the Copenhagen Interpretation of Quantum Mechanics