Summary
An introduction to the theory of random Hamiltonians is given with special emphasis on the statistics of energy level spacings. The physical origin of the repulsion of energy levels is discussed. The importance of the symmetries of the system for level repulsion is emphasized. Several recent physical examples of level statistics of disordered quantum coherent systems are discussed including localized and metallic systems, the universal behaviour of the level spacing distribution at the disorder-induced metal-insulator transition and the fluctuations in the Coulomb oscillations of the conductance of quantum dots.
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Kramer, B. (2002). Introduction to Energy Level Statistics. In: Computational Statistical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04804-7_14
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DOI: https://doi.org/10.1007/978-3-662-04804-7_14
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