Applications of the random matrix ensembles to the quantum statistical systems

Abstract

The random matrix ensembles are applied to the quantum statistical 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.

arXiv comment5 pages; presented as a poster at "Field Theory and Statistical Mechanics", International Conference; June 10, 2002 - June 15, 2002; Department of Physics, University of Rome "La Sapienza"; Rome, Italy