Symmetry deduction from spectral fluctuations in complex quantum systems

S. Harshini Tekur, M. S. Santhanam

Published 2018-08-26Version 1

The spectral fluctuations of complex quantum systems are known to be consistent with that from random matrices, but only for desymmetrized spectra. This impedes the analysis of experimentally measured or computed spectra. We show that for a spectrum composed of k > 0 independent sequences, its k-th order spacing ratio distribution is identical to its nearest neighbor counterpart with modified Dyson index $\beta$ = k. The fluctuation character and symmetry structure of any arbitrary sequence of levels can be inferred from its higher order fluctuations without desymmetrization. This is shown for random matrices and also verified using measured levels of Ta nucleus, quantum billiards and spin chains.