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49 pages, 1997, preprint of Les Houches, Session LXIII, 1995; arxiv: cond-mat\9602/9602071v2;arXiv:cond-mat/9602071v2 [cond-mat.

Abstract:

These are notes of a first course on computations of energy spectra and electronic properties in disordered solids, such as conducting metallic glasses that exhibit Anderson localization and other interesting related quantum phenomena. Quantum spectra of disordered, metallic solids are expressed mathematically with the Random Matrix Theory (RMT). Selected highlights of lectures from the course contents notes are: "2. Metal as a quantum chaotic system;3. Level correlations in a disordered metal, p. 13 3.1. Weak-localization, p.15 3.2. Semi-classical description of energy levels correlations, p.16 3.3. Breakdown of time-reversal symmetry, Aharonov-Bohm flux, p.20 5. Conductance and spectrum: p.34 5.1. The Thouless formula and its extensions: p. 35 5.2. Universal Conductance Fluctuations." Coupled with intuitive illustrations and examples it is a valuable course on applications of mathematical physics to non-crystalline or disordered solids, metals and metallic glasses, leading to quantum supergroup applications to RMT and spectral calculations. The Metal-Insulator transition is shown to be characterized by a distribution which is intermediate between Wigner and Poisson distributions. The thermodynamic properties such as the magnetization of ballistic mesoscopic conductors, where the disorder is weak raises new and very interesting questions that may be resoved by RMT-based computations. Free, on line course notes download at: http://arxiv.org/PS_cache/cond-mat/pdf/9602/9602071v2.pdf

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arXiv:cond-mat/9602071v2 [cond-mat.mes-hall] http://arxiv.org/PS_cache/cond-mat/pdf/9602/9602071v2.pdf Open access arXiv:cond-mat/9602071v2 [cond-mat.mes-hall] http://arxiv.org/PS_cache/cond-mat/pdf/9602/9602071v2.pdf

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