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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Gaussian orthogonal ensemble statistics in a microwave stadium billiard with chaotic dynamics: Porter-Thomas distribution and algebraic decay of time correlations.
H. Alt,H.-D. Gräf,H. L. Harney,R. Hofferbert,H. Lengeler,Achim Richter,P. Schardt,Hans A. Weidenmüller +7 more
TL;DR: In this article, the complete set of resonance parameters for 950 resonances of a superconducting microwave cavity connected to three antennas has been measured and the partial widths are found to follow a Porter-Thomas distribution.
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Distribution of local densities of states, order parameter function, and critical behavior near the Anderson transition
TL;DR: In this paper, the exact relations between the order parameter function of the Anderson transition and the distributions of local densities of states (LDSO) and eigenfunction amplitudes are derived.
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Wave Propagation in a One-Dimensional Random Medium
TL;DR: In this article, the wave propagation in a slab of random medium is considered and the index of refraction is assumed to fluctuate randomly about a mean value, the fluctuations being small.
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Approach to ergodicity in quantum wave functions
TL;DR: A semiclassical theory is developed that relates the rate of approach to the decay of certain classical fluctuations in uniformly hyperbolic systems and predicts a slower decay due to sticking in marginally unstable regions.
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Universalities in the spectra of disordered and chaotic systems.
TL;DR: A nonperturbative expression is derived for the autocorrelator of density-of-states fluctuations for systems taken from both the unitary and orthogonal ensembles, showing that the dependence on these two parameters can be removed by a rescaling.