Spectral fluctuation and correlation structure of δ(n) statistics in the spectra of interacting trapped bosons

It is a well-known fact that the statistical behaviors of level fluctuation and level correlation in the energy-level spectra are the most efficient tool to characterize quantum chaos in nonintegrable quantum systems. The system of interacting trapped bosons is a complex system where the low-lying energy levels are highly influenced by the level repulsion. In this case, interatomic interaction is a dominating fact with strong level correlation between distant levels. Here we numerically calculate the correlation function, number variance, and Dyson-Mehta least-square deviation for the low-lying levels for a few thousand interacting trapped bosons, and our data show good analogy with the Gaussian orthogonal ensemble (GOE) results with a signature of chaos. In the next part of our study, the energy spectrum of these low-lying levels is considered as a discrete signal and the fluctuation of the excitation energy is considered as discrete time series. Then we calculate numerically the height-height correlation function for different order of momentum. In our study logarithmic correlation structure is found instead of multiscaling structure, and we observe that spectral statistics are compatible with those of GOE.