Applications of the random matrix ensembles to the quantum statistical\n systems

2002/12/12 by M. M. Duras, Maciej M. Duras, Duras, Maciej M.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Quantum chaos and dynamical systems #Random Matrices and Applications #Scientific Research and Discoveries #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0212287

5 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

openalex publication_date 2002/12/12 · arxiv created 2003/07/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The random matrix ensembles are applied to the quantum statistical systems.\nThe quantum systems are studied using the finite dimensional real, complex and\nquaternion Hilbert spaces of the eigenfunctions. The linear operators\ndescribing the systems act on these Hilbert spaces and they are treated as\nrandom matrices in generic bases of the eigenfunctions. The random\neigenproblems are presented and solved. Examples of random operators are\npresented with connection to physical problems.\n

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