We derive the explicit expression for the distribution of resonance widths ina chaotic quantum system coupled to continua via M equivalent open channels. Itdescribes a crossover from the $\chi^2$ distribution (regime of isolatedresonances) to a broad power-like distribution typical for the regime ofoverlapping resonances. The first moment is found to reproduce exactly theMoldauer-Simonius relation between the mean resonance width and thetransmission coefficient. This fact may serve as another manifestation ofequivalence between the spectral and the ensemble averaging.
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机译：我们导出了通过M个等效的开放通道耦合到contina的混沌量子系统中共振宽度分布的明确表达式。它描述了从$ \ chi ^ 2 $分布（孤立共振的状态）到典型的重叠共振状态的宽幂形分布的交叉。发现第一矩精确地再现了平均谐振宽度和透射系数之间的Moldauer-Simonius关系。这个事实可以作为频谱平均和集合平均之间等效的另一种表现。
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