ICCS2004 Application Submission/Review

Abstract for
"Level Statistics of Complex Systems"

The dynamical studies of various complex systems require a statistical information about eigenvalues and eigenfunctions of the generators of the dynamics. It is very useful, if possible, to identify a common mathematical structure among them and analyze it to gain information. Our successful search in this direction leads to Calogero-Sutherland Hamiltonian, a one-dimensional quantum Hamiltonian with inverse-square interaction, as the common base. This is because both, the eigenvalues of complex generators, and, a general state of Calogero Hamiltonian, evolve in an analogous way for arbitrary initial conditions. The varying nature of the complexity is reflected in different form of the evolution parameter in each case. A complete investigation of Calogero Hamiltonian can then help us in the spectral analysis of complex systems.