Open quantum systems and Random Matrix Theory
Declan Mulhall
TL;DR
This paper investigates how coupling to the continuum affects the spectral statistics of open quantum systems using Random Matrix Theory, revealing a super-radiant transition and signatures of missed levels.
Contribution
It introduces a simple model for open quantum systems analyzed with RMT, highlighting the spectral effects of system-environment coupling and the super-radiant transition.
Findings
Observation of super-radiant transition
Changes in level spacing and $\Delta_3(L)$ with coupling strength
Signatures of missed levels during transition
Abstract
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 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 statistic exhibit the signatures of missed levels.
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