Deviations from Berry--Robnik Distribution Caused by Spectral Accumulation

By extending the Berry–Robnik approach for the nearly integrable quantum systems,\cite{[1]} we propose one possible scenario of the energy level spacing distribution that deviates from the Berry–Robnik distribution. The result described in this paper implies that deviations from the Berry–Robnik distribution would arise when energy level components show strong accumulation, and otherwise, the level spacing distribution agrees with the Berry–Robnik distribution.