Bound State Internal Interactions as a Mechanism for Exponential Decay

TL;DR

The paper addresses the foundational question of why bound quantum systems exhibit approximate exponential decay. It proposes a model in which internal binding interactions among bound-state components, mediated by background fields, act like continuous measurements, producing an exact exponential non-decay probability $P_u(t)=e^{-t/τ}$ and a time-independent Fermi's Golden Rule for decay rates. By separating internal binding dynamics from couplings to decay products, it explains how Lorentzian decay lineshapes can emerge without invoking non-Hermitian Hamiltonians and clarifies the continuum between Quantum Zeno control and uncontrolled internal dynamics. The framework has potential implications for quantum engineering, suggesting routes to prolong lifetimes by engineering internal interactions or the environment, and for understanding observed deviations in certain systems. Overall, it provides a conceptually transparent account of exponential decay in bound systems and a practical method to compute decay rates across channels.

Abstract

We hypothesize that the binding interactions among the components of bound systems and the background fields, sometimes known as virtual particle exchange, affect the state of the systems as do typical scattering interactions. Then with the assumption that the interior environment of unstable particles is disordered, we derive in the limit of continuous binding both an exactly exponential non-decay probability and Fermi's Golden Rule for the decay rates. The result suggests resolutions to several long-standing theoretical challenges associated with exponential decay in quantum mechanics, without appealing directly to non-Hermitian, approximate Hamiltonians or complex energies. It also contributes to a conceptual understanding of the continuum between controlled interactions that induce deviations from exponential decay, such as those in the Quantum Zeno Effect, and the uncontrolled internal dynamics of excited atoms and nuclei, which exhibit no such deviations. Finally, we examine how the binding interactions responsible for the general exponential character of decay for bound systems differ from the couplings with decay products that control decay rates, providing insight into challenges in quantum computing and information processing.