In general, the physical systems are quite complex in nature. Our approximate knowledge of the complicated interactions in these systems manifests itself by a randomization of various generators of the dynamics. The operators associated with wave dynamics e.g Hamiltonian, electromagnetic waves in a microwave cavity, or signals in a brain etc. can therefore be modeled by random matrices.
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 mathematcal structure among all the ensembles and analyze it to gain information about the ensemble-properties. Our successful search in this direction leads to Calogero Hamiltonian, a quantum hamiltonian with inverse-square interaction, as the common base.
As an example, we will discuss the application of the above approach to disordered systems with or without electon-electron interactions.