Classical limit of the quantum Zeno effect

TL;DR

This paper demonstrates that the quantum Zeno effect, where frequent measurements inhibit a quantum system's evolution, disappears in the classical limit, confirming it as a purely quantum phenomenon without a classical counterpart.

Contribution

The paper provides a semiclassical analysis showing the quantum Zeno effect vanishes at all orders as Planck's constant approaches zero, establishing its purely quantum nature.

Findings

Quantum Zeno effect is confined in a subspace due to frequent measurements.

The effect vanishes in the classical limit (Planck constant to zero).

The phenomenon is purely quantum, with no classical analog.

Abstract

The evolution of a quantum system subjected to infinitely many measurements in a finite time interval is confined in a proper subspace of the Hilbert space. This phenomenon is called "quantum Zeno effect": a particle under intensive observation does not evolve. This effect is at variance with the classical evolution, which obviously is not affected by any observations. By a semiclassical analysis we will show that the quantum Zeno effect vanishes at all orders, when the Planck constant tends to zero, and thus it is a purely quantum phenomenon without classical analog, at the same level of tunneling.