Maciej M. Duras
Published 2003-03-13, updated 2003-07-02Version 4
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. 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: 6 pages; "Fluctuations and Noise in Photonics and Quantum Optics", D. Abbott, J. H. Shapiro, Y. Yamamoto, Eds.; Proceedings of SPIE; Society of Photo-optical Instrumentation Engineers, Bellingham, WA, USA, Vol. 5111, 456-459 (2003)
Universal singularity at the closure of a gap in a random matrix theory
Fluctuations of Quantum Statistical Two-Dimensional Systems of Electrons
The effect of quantum fluctuations on the coloring of random graphs
