Effect of the resonance spectra in the propagation of two decaying entangled particles

TL;DR

This paper provides an exact analytical study of how resonance spectra influence the decay and propagation of entangled particles, revealing conditions under which common approximations hold or fail.

Contribution

It introduces an exact solution for the decay of entangled particles and analyzes the impact of resonance spectra on their propagation, highlighting the limitations of the two resonance level approximation.

Findings

Sharp high energy resonances disrupt exponential decay regimes.

Broad high energy resonances are well described by the two resonance approximation.

Resonance spectra significantly affect the decay dynamics of entangled particles.

Abstract

An exact analytical solution of the decaying wave function of two identical noninteracting particles, which are entangled by spatial symmetry, is used to analyze the effect of the resonance spectra in the propagation of the decaying probability density outside the interaction potential region. We find, using exactly solvable problems, that a usual approximation that considers the two resonance levels associated with the initial states, is affected substantially in the case of sharp high energy resonances by disrupting the pure exponential decaying regime exhibited by the two resonance level approximation, whereas for broad high energy resonances, we find that the probability density profile is well described by the two resonance approximation.