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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Area laws in a many-body localized state and its implications for topological order
Bela Bauer,Chetan Nayak +1 more
TL;DR: In this paper, it was shown that a single energy eigenstate of a Hamiltonian can be adiabatically connected to a state of a non-interacting Anderson insulator.
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Characterizing dynamics with covariant Lyapunov vectors.
TL;DR: A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced, which allows us to address fundamental questions such as the degree of hyperbolicity, which can be quantified in terms of the transversality of these intrinsic vectors.
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Superconductor-insulator quantum phase transition
TL;DR: The current understanding of the superconductor-insulator transition is discussed level by level in a cyclic spiral-like manner in this article, with a special discussion on phenomenological scaling theories.
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Spectra of complex networks.
TL;DR: It is shown that spectra of locally treelike random graphs may serve as a starting point in the analysis of spectral properties of real-world networks, e.g., of the Internet.
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Geometrical structure of Laplacian eigenfunctions
TL;DR: The main focus is put onto multiple intricate relations between the shape of a domain and the geometrical structure of eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundary condition.
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.