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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Statistics of conductance fluctuations in quantum dots.
TL;DR: Using the supersymmetry method, the conductance distribution function for a system of noninteracting electrons is calculated for the first time exactly.
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Boundary Conditions at the Mobility Edge
TL;DR: In this paper, it was shown that the universal behavior of the spacing distribution of nearest energy levels at the metal-insulator Anderson transition is indeed dependent on the boundary conditions and that the spectral rigidity of wave functions in the bulk is not affected by boundary conditions.
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Chaos, Interactions, and Nonequilibrium Effects in the Tunneling Resonance Spectra of Ultrasmall Metallic Particles
TL;DR: In this paper, the authors explain the observation of clusters in the tunneling resonance spectra of small metallic particles of few nanometer size, identified with one excited single electron state of the metal particle, shifted as a result of the different nonequilibrium occupancy configurations of the other single electron states.
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Random Walks through the Ensemble: Linking Spectral Statistics with Wave-Function Correlations in Disordered Metals.
TL;DR: A random walk in the ensemble of impurity configurations is used to generate a Brownian motion model for energy levels in disordered conductors and the resulting Langevin equation relates spectral statistics to eigenfunction correlations.
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The Laplacian on a random one-dimensional lattice
TL;DR: In this paper, the spectrum of the Laplacian on a random one-dimensional lattice is studied and the authors find as expected localisation effects throughout the whole range.