Abstract
After reviewing the description of an unstable state in the framework of nonrelativistic Quantum Mechanics (QM) and relativistic Quantum Field Theory (QFT), we consider the effect of pulsed, ideal measurements repeated at equal time intervals on the lifetime of an unstable system. In particular, we investigate the case in which the ‘bare’ survival probability is an exact exponential (a very good approximation in both QM and QFT), but the measurement apparatus can detect the decay products only in a certain energy range. We show that the Quantum Zeno Effect can occur in this framework as well.
Highlights
The study of decays is important in atomic, nuclear, and particle physics
It is well established both in Quantum Mechanics (QM) [1,2,3] and in Quantum Field Theory (QFT) [4, 5] that the survival probability p(t) of an unstable state |S is never exactly an exponential function: deviations at short as well as at long times take place
In this work we have first reviewed the emergence of the Breit-Wigner limit, and of the exponential decay, in both QM and QFT
Summary
The study of decays is important in atomic, nuclear, and particle physics. Quite remarkably, weak decays of nuclei (e.g. double-β decays with lifetime ∼ 1021 y), and fast decays of hadrons (with lifetime ∼ 10−22 sec) are characterized by very different decay times, the basic phenomenon is the same: a coupling of an initial unstable state to a continuum of final states, which results in an irreversible quantum transition (infinite Poincare’ time). It has been found that the QZE occurs for repeated pulsed bangbang measurements in which the collapse of the wave function takes place; the outcomes of bang-bang and continuous measurements are in general different (i.e., the Schulman relation does not hold), a property which has interesting implications for what concerns the interpretation of QM. In these proceedings we first review the decay law both in QM and in QFT in Sec. 2, where we concentrate on the derivation of the exponential limit.
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