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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On the multifractal nature of fully developed turbulence and chaotic systems
TL;DR: In this paper, the authors review the concept of multifractal sets in both turbulent flows and dynamical systems using a generalisation of the beta-model and propose that the energy dissipation of three-dimensional turbulent flow is concentrated on a set with non-integer Hausdorff dimension.
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Chaos, Quantum Recurrences, and Anderson Localization
TL;DR: In this paper, it was shown that the local quasi-energy spectrum of the rotator problem is discrete and that its wave function is almost periodic in time, which allows one to understand on physical grounds some numerical results recently obtained in the context of rotator problems.
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Universal conductance fluctuations in metals: Effects of finite temperature, interactions, and magnetic field.
TL;DR: In this article, the conductance of any metallic sample has been shown to fluctuate as a function of chemical potential, magnetic field, or impurity configuration, independent of sample size and degree of disorder at zero temperature.
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Scaling theory of the integer quantum Hall effect
TL;DR: In this paper, a brief review of the present understanding of the transitions between integer quantized plateaus of the Hall conductivity in two-dimensional disordered systems in a strong magnetic field is given.