Paraphrase the following text using more academic and scientific language Use a neutral tone and avoid repetitions of words and phrases：Subsequently we establishe the correlation between momentum vari

We then established a correlation between the variance of momentum and the probability of survival. Momentum variance is a physical quantity that provides an intuitive measure of the diffusion of momentum in a dynamic system. It is defined as the average of the squared difference between the momentum at time N and the initial momentum, as expressed in the equation above. The momentum variance is indicative of the degree of extension of the momentum wave function with respect to the average momentum, considering all initial states and noise sequences, including colored and temporal noise.