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We present a statistical analysis of eigenenergies and discuss severalmeasures of spectral fluctuations and spectral correlations for the van derWaals clusters of different sizes. We show that the clusters become more andmore complex with increase in cluster size. We study nearest-neighbour levelspacing distribution $P(s)$, the level number variance $\Sigma^2(L)$, and theDyson-Mehta $\Delta_3-$statistics for various cluster sizes. For large clusterswe find that although the Bohigas-Giannoni-Schmit (BGS) conjecture seems to bevalid, it does not exhibit true signatures of quantum chaos. Howevercontrasting conjecture of Berry and Tabor is observed with smaller clustersize. For small number of bosons, we observe the existence of large number ofquasi-degenerate states in low-lying excitation which exhibits the Shnirelmanpeak in $P(s)$ distribution. We also find a narrow region of intermediatespectrum which can be described by semi-Poisson statistics whereas the higherlevels are regular and exhibit Poisson statistics. These observations arefurther supported by the analysis of the distribution of the ratio ofconsecutive level spacings $P(r)$ which is independent of unfolding procedureand thereby provides a tool for more transparent comparison with experimentalfindings than $P(s)$. Thus our detail numerical study clearly shows that thevan der Waals clusters become more correlated with the increase in clustersize.

Level spacing statistics and spectral correlations in the diffuse van der Waals clusters