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Open quantum systems and Random Matrix Theory

A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the $Δ_3(L)$ statistic, width distribution and level spacing are examined as a function of the strength of this coupling. A super-radiant transition is observed, and it is seen that as it is formed, the level spacing and $Δ_3(L)$ statistic exhibit the signatures of missed levels.

preprint2015arXivOpen access
Declan Mulhall
nucl-th
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Declan Mulhall

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