Time-Dependent Quantum Weak Values: Decay Law for Post-Selected States

TL;DR

This paper extends the understanding of quantum decay laws by analyzing weak measurements on time-dependent ensembles, revealing a generalized decay law influenced by post-selection timing and final state choice.

Contribution

It introduces a generalized decay law for post-selected quantum states, broadening the traditional exponential decay model through weak measurement analysis.

Findings

Standard decay law is a special case of the generalized law.

Decay behavior depends on post-selection timing and final state.

Illustrations demonstrate the impact of different post-selection choices.

Abstract

Weak measurements offer new insights into the behavior of quantum systems. Combined with post-selection, quantum mechanics predicts a range of new experimentally testable phenomena. In this paper I consider weak measurements performed on time-dependent pre- and post-selected ensembles, with emphasis on the decay of excited states. The results show that the standard exponential decay law is a limiting case of a more general law that depends on both the time of post-selection and the choice of final state. The generalized law is illustrated for two interesting choices of post-selection.