Paraphrase the following text using more academic and scientific language Use a neutral tone and avoid repetitions of words and phrases对于具有不同初末态的生存概率$A_rs$由于不同本征态的局域化中心不同且局域化长度较窄因此非对角项的$A_rs$近似认为是0

The survival probability $A_{rs}$ for different initial and final states is deemed to be approximately zero for non-diagonal terms, due to the distinct localization centers of different eigenstates and the narrow localization lengths associated with them.