Alternative technique for complex spectra analysis

The choice of a suitable random matrix model of a complex system is very se nsitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wid e range of random matrix ensembles which is not an easy task. It is highly desirable, if possible, to identify a common mathematical structure among a ll the ensembles and analyze it to gain information about the ensemble prop erties. Our successful search in this direction leads to the Calogero Hamil tonian. a one-dimensional quantum Hamiltonian with inverse-square interacti on, as the common base. This is because both the eigenvalues of the ensembl es and a general state of the Calogero Hamiltonian evolve in an analogous w ay for arbitrary initial conditions. The varying nature of the complexity i s reflected in different forms of the evolution parameter in each case. A c omplete investigation of the Calogero Hamiltonian can then help us in the s pectral analysis of complex systems.