Derivation of the universal decay cascade distribution

TL;DR

This paper provides a detailed derivation of the universal decay cascade probability distribution, clarifying the mathematical foundations and connections between different limiting cases, as originally stated in prior work.

Contribution

It offers an explicit solution to recurrence relations and demonstrates the connections between solutions in various limits, enhancing understanding of the decay cascade distribution.

Findings

Explicit solutions to recurrence relations

Connections between different limit solutions

Clarification of the decay cascade distribution derivation

Abstract

A detailed derivation of the decay cascade probability distribution stated in Eqs. (4)-(6) and (11) of Phys. Rev. Lett. 104, 186805 (2010) [arXiv:0901.4102] by Kashcheyevs and Kaestner is provided. Recurrence relations are solved explicitly and connections between solutions in different limits are demonstrated.