Quantum fluctuations and random matrix theory

Details Quantum fluctuations and random matrix theory Quantum fluctuations and random matrix theory

2003-03-13

arxiv.org/abs/cond-mat/0303262v4

Physics

Condensed Matter

Statistical Mechanics

6 pages; "Fluctuations and Noise in Photonics and Quantum Optics", D. Abbott, J. H. Shapiro, Y. Yamamoto, Eds.; Proceedings of

Scientific paper

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.

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