In this paper, we investigate non-single exponential photoluminescence decays in various disordered condensed-matter systems. For such materials, two formulas for the average lifetime of system's excited state are commonly used in the analysis of experimental data. In many cases, the choice of formula is arbitrary and lacks a clear physical justification. For this reason, our main goal is to show that the choice of correct mathematical formula should be based on the interpretation of measured photoluminescence decay curve. It is shown that depending on the investigated system, after appropriate normalization, photoluminescence decay curve can represent either a survival probability function or a probability density function of lifetime and for this reason two different formulas for the average lifetime are required. It is also shown that, depending on luminescence quantum yield, some information on the probability density function of lifetime can be lost in the process of measurement, which results in underestimated values of average lifetime. Finally, we provide an interpretation of total decay rate distributions which are frequently obtained by phenomenological modeling of non-single exponential photoluminescence decays.

中文翻译：

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关于显示非单指数光致发光衰减的发射体集合的适当平均寿命公式的选择

在本文中，我们研究了各种无序凝聚态系统中的非单指数光致发光衰减。对于此类材料，通常在实验数据分析中使用两个系统激发态平均寿命公式。在许多情况下，公式的选择是任意的，缺乏明确的物理理由。出于这个原因，我们的主要目标是表明正确数学公式的选择应该基于对测量光致发光衰减曲线的解释。结果表明，根据所研究的系统，经过适当的归一化后，光致发光衰减曲线可以表示寿命的生存概率函数或概率密度函数，因此需要两种不同的平均寿命公式。还表明，根据发光量子产率，在测量过程中可能会丢失一些关于寿命概率密度函数的信息，从而导致平均寿命值被低估。最后，我们提供了对总衰减率分布的解释，这些分布经常通过非单指数光致发光衰减的现象学建模获得。