Survival Probability of an Excited State in the Bixon-Jortner Model

TL;DR

This study investigates the survival probability dynamics of an excited state in the Bixon-Jortner model, revealing initial exponential decay followed by oscillations due to state repopulation effects.

Contribution

It provides numerical analysis of survival probability behavior in the Bixon-Jortner model, highlighting the effects of energy level separation and transition strength on state dynamics.

Findings

Initial exponential decay of survival probability

Repopulation of the excited state over time

Oscillatory behavior in survival probability

Abstract

When the initial state of a quantum mechanical system is an excited state, then it is expected that the occupation, or survival, probability of that state will decrease. This is studied numerically within the Bixon-Jortner model, which was introduced to model intramolecular radiationless transitions. Here a finite set of states is used and for a fixed number of states, the parameters of the model are the energy level separation and the strength of the transition matrix element. All three of these are varied to see their effects on the survival probability. After a short interval of time, the survival probability decay is often found to be an exponential. But the survival probability is then found to increase with further time and then decrease in a pattern that continues in time. This repopulation is a general feature when a countable set of states is present.