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The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of random matrix ensembles which is not an easy task. It is highly desirable, if possible, to identify a common mathematical structure among all the ensembles and analyze it to gain information about the ensemble properties. Our successful search in this direction leads to the Calogero Hamiltonian, a one-dimensional quantum Hamiltonian with inverse-square interaction, as the common base. This is because both the eigenvalues of the ensembles and a general state of the Calogero Hamiltonian evolve in an analogous way for arbitrary initial conditions. The varying nature of the complexity is reflected in different forms of the evolution parameter in each case. A complete investigation of the Calogero Hamiltonian can then help us in the spectral analysis of complex systems.

Alternative technique for complex spectra analysis