Maciej M. Duras
Published 2002-12-12, updated 2003-07-03Version 2
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.
Comments: 5 pages; presented as a poster at "Control, Communication, and Synchronization in Chaotic Dynamical Systems"; Worskshop: October 14th, 2001 - October 19th, 2001; November 11th, 2001 - November 16th, 2001; Seminar: October 14th, 2001 - November 23rd, 2001; Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
Applications of the random matrix ensembles to the quantum statistical systems
Applications of Random Matrix Ensembles in Nuclear Systems
Superstatistics: Recent developments and applications
