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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Localization and Universality of Eigenvectors in Directed Random Graphs.
Fernando L. Metz,Izaak Neri +1 more
TL;DR: A general theory for the statistics of the right eigenvector components in directed random graphs with a prescribed degree distribution and with randomly weighted links is presented and it is shown that in the high connectivity limit the distribution of theright eigen vector components is solely determined by the degree distribution.
Conformal Bootstrap in Liouville Field Theory
TL;DR: In this article, Liouville Field Theory (LFT) was shown to reproduce some of the predictions of the matrix model approach, in particular the scaling behavior, genus one partition functions, and integrated correlation functions.
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Correlation Functions of Impedance and Scattering Matrix Elements in Chaotic Absorbing Cavities
TL;DR: In this article, the energy correlation functions of different matrix elements of impedance or scattering matrices for systems with preserved or broken time-reversal symmetry were calculated within the random matrix approach and the obtained results are valid at any number of arbitrary open scattering channels and arbitrary absorption.
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Spectral behavior of partially pumped weakly scattering random lasers
Jonathan Andreasen,Hui Cao +1 more
TL;DR: Stochastic noise is incorporated in the numerical simulation of weakly scattering random lasers, which qualitatively captures lasing phenomena that have been observed experimentally, and may facilitate incremental observation of lasing in smaller-threshold modes in the emission spectrum with fine adjustments of the pumping rate.
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Spectral statistics, finite-size scaling and multifractal analysis of quasiperiodic chain with p-wave pairing
TL;DR: In this paper, the spectral and wave function properties of a one-dimensional incommensurate system with p-wave pairing were studied and a series of particular properties in its ciritical region were revealed.
References
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Methods of Theoretical Physics. By P.M. Morse and H. Feschbach. 2vols., Pp.xxii, 1978. 120s. each vol. 1953.(McGraw-Hill)
Book
Wave propagation and scattering in random media
TL;DR: This IEEE Classic Reissue presents a unified introduction to the fundamental theories and applications of wave propagation and scattering in random media and is expressly designed for engineers and scientists who have an interest in optical, microwave, or acoustic wave propagate and scattering.
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Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
TL;DR: In this paper, it was shown that the conductance of disordered electronic systems depends on their length scale in a universal manner, and asymptotic forms for the scaling function were obtained for both two-dimensional and three-dimensional systems.