Exponential Decay and Fermi's Golden Rule from an Uncontrolled Quantum Zeno Effect

TL;DR

This paper revises the quantum Zeno effect theory to account for realistic, uncontrolled measurements, explaining exponential decay and deriving Fermi's Golden Rule in a more conceptually straightforward manner.

Contribution

It introduces a modified theory of the Quantum Zeno Effect that incorporates uncontrolled measurements, leading to new insights into decay processes and a derivation of Fermi's Golden Rule.

Findings

Uncontrolled monitoring causes exponential decay at all times.

Continuous ideal measurements only inhibit decay in special cases.

Decay rates partition into sums for multiple channels, matching observations.

Abstract

We modify the theory of the Quantum Zeno Effect to make it consistent with the postulates of quantum mechanics. This modification allows one, throughout a sequence of observations of an excited system, to address the nature of the observable and thereby to distinguish survival from non-decay, which is necessary whenever excited states are degenerate. As a consequence, one can determine which types of measurements can possibly inhibit the exponential decay of the system. We find that continuous monitoring taken as the limit of a sequence of ideal measurements will only inhibit decay in special cases, such as in well-controlled experiments. Uncontrolled monitoring of an unstable system, however, can cause exponentially decreasing non-decay probability at all times. Furthermore, calculating the decay rate for a general sequence of observations leads to a straightforward derivation of Fermi's Golden Rule, that avoids many of the conceptual difficulties normally encountered. When multiple decay channels are available, the derivation reveals how the total decay rate naturally partitions into a sum of the decay rates for the various channels, in agreement with observations. Continuous and unavoidable monitoring of an excited system by an uncontrolled environment may therefore be a mechanism by which to explain the exponential decay law.