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A random matrix model with localization and ergodic transitions
Motivated by the problem of many-body localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig–Porter…
Nonergodic Phases in Strongly Disordered Random Regular Graphs.
A new generalized population dynamics that is able to detect the violation of ergodicity of the delocalized states within the Abou-Chakra, Anderson, and Thouless recursive scheme is suggested.
Fractal superconductivity near localization threshold
Dynamical scaling for critical states: Validity of Chalker's ansatz for strong fractality
The dynamical scaling for statistics of critical multifractal eigenstates proposed by Chalker is analytically verified for the critical random matrix ensemble in the limit of strong multifractality…
Supersymmetric virial expansion for time-reversal invariant disordered systems
We develop a supersymmetric virial expansion for two-point correlation functions of almost diagonal Gaussian random matrix ensembles (ADRMT) of the orthogonal symmetry. These ensembles have multiple…
Localized to extended states transition for two interacting particles in a two-dimensional random potential
We show by a numerical procedure that a short-range interaction u induces extended two-particle states in a two-dimensional random potential. Our procedure treats the interaction as a perturbation…
Level compressibility in a critical random matrix ensemble: the second virial coefficient
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Phase Transition in Coulomb Glasses
Capsize of polarization in dilute photonic crystals
A theoretical model of dilute photonic crystal, based on Maxwell’s equations with a spatially dependent two dimensional inhomogeneous dielectric permittivity, shows that the polarization's rotation can be explained by an optical splitting parameter appearing naturally in Maxwell's equations for magnetic or electric fields components.
Lévy flights and multifractality in quantum critical diffusion and in classical random walks on fractals.
- V. Kravtsov, O. Yevtushenko, P. Snajberk, E. Cuevas
- PhysicsPhysical review. E, Statistical, nonlinear, and…
- 31 May 2012
It is found that the long-range nature of the Hamiltonian is a common root of both multifractality and Lévy flights, which show up in the power-law intermediate- and long-distance behaviors, respectively, of the density correlation function.