Statistics of energy levels and eigenfunctions in disordered systems
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TLDR
In this article, a review of recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples is presented, with emphasis on low-dimensional (quasi-1D and 2D) systems.About:
This article is published in Physics Reports.The article was published on 2000-03-01 and is currently open access. It has received 557 citations till now. The article focuses on the topics: Eigenfunction & Mesoscopic physics.read more
Citations
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Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states
TL;DR: In this paper, it was shown that in the absence of coupling of the electrons to any external bath dc electrical conductivity exactly vanishes as long as the temperature T does not exceed some finite value Tc.
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Anderson Transitions
TL;DR: In this paper, the physics of Anderson transition between localized and metallic phases in disordered systems is reviewed, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states.
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Transport and Anderson localization in disordered two-dimensional photonic lattices
TL;DR: The experimental observation of Anderson localization in a perturbed periodic potential is reported: the transverse localization of light caused by random fluctuations on a two-dimensional photonic lattice, demonstrating how ballistic transport becomes diffusive in the presence of disorder, and that crossover to Anderson localization occurs at a higher level of disorder.
Sous la direction de
Françoise Port A Els,M. M Eyers +1 more
TL;DR: Mostafa Adimy as mentioned in this paper Directeur de Recherches à l’INRIA Dir. de thèse Ionel S. CIUPERCA Mâıtre de Conférence à l'Université Lyon 1 Examinateur Michael C. MACKEY Directeur of Recherche et al.
Book
Eigenvalue Distribution of Large Random Matrices
Leonid Pastur,Mariya Shcherbina +1 more
TL;DR: Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and related sciences as mentioned in this paper, which is a good reference for researchers in various areas of mathematics and mathematical physics.
References
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Path integrals for waves in random media
TL;DR: In this paper, the problem of wave propagation in a random medium is formulated in terms of Feynman's path integral, which turns out to be a powerful calculational tool.
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Scaling properties of localization in random band matrices: A sigma -model approach.
TL;DR: It is proved that ${\mathit{b}}^{2}$/N, N being the matrix size, is the relevant scaling parameter when the mean value of diagonal elements increases linearly along the diagonal an extra scaling parameter arises.
Book
Handbook of integral transforms of higher transcendental functions : theory and algorithmic tables
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Gutzwiller's Trace Formula and Spectral Statistics: Beyond the Diagonal Approximation.
Eugene Bogomolny,Jon P Keating +1 more
TL;DR: This work calculates the 2-point spectral correlation function for classically chaotic systems in the semiclassical limit using Gutzwiller’s trace formula and finds the behavior is similar to that recently discovered to hold for disordered systems using nonperturbative supersymmetric methods.