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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Correlations Between Ground and Excited State Spectra of a Quantum Dot
TL;DR: The ground and excited state spectra of a semiconductor quantum dot with successive electron occupancy were studied with linear and nonlinear magnetoconductance measurements as mentioned in this paper, and a direct correlation was observed between the mth excited state of the N-electron system and the ground state for m up to 4.
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Breakdown of multifractal behavior in diffusion-limited aggregates.
Raphael Blumenfeld,Amnon Aharony +1 more
TL;DR: In this article, a phase transition to non-multifractal behavior of the qth moment of diffusion-limited aggregates is discussed, and the authors show that for aggregates of size L, this transition splits into two at q = 0.
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Spectral fluctuation properties of Hamiltonian systems: the transition region between order and chaos
TL;DR: In this article, the authors studied the spectral fluctuation properties of a class of Hamiltonian systems with two degrees of freedom, and found that the observed spectral fluctuations can be reproduced by a random-matrix model which depends on one parameter only.
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Spectral statistics: From disordered to chaotic systems.
TL;DR: The relation between disordered and chaotic systems is investigated by identifying the diffusion operator of the disordered systems with the Perron-Frobenius operator in the general case and the two-point level density correlator and the structure factor for general chaotic systems are calculated and characterized.
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Statistics of conductance oscillations of a quantum dot in the Coulomb-blockade regime
TL;DR: In this paper, the fluctuations and the distribution of the conductance peak spacings of a quantum dot in the Coulomb blockade regime are studied and compared with the predictions of random matrix theory (RMT).