Dresden 2006 – scientific programme

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DY: Dynamik und Statistische Physik

DY 46: Poster

DY 46.84: Poster

Thursday, March 30, 2006, 16:00–18:00, P1

Statistical Studies of Complex Systems: A Random Matrix Approach — •Pragya Shukla — Department of PHysics, IIT Kharagpur-721302, West Bengal, India

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 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 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 Dyson’s Brownian motion model as the common base. This also reveals the deep level of universality hidden underneath the world of complex sysetms.