Various applications of the random matrix ensembles to the quantum chaotic systems

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

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5 pages; presented as a poster at "Control, Communication, and Synchronization in Chaotic Dynamical Systems"; Worskshop: Octob

Scientific paper

The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the systems act on these Hilbert spaces and they are treated as random matrices in generic bases of the eigenfunctions. The random eigenproblems are presented and solved. Examples of random operators are presented with connection to physical problems.

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