相关论文: Dynamical delocalization in random Landau Hamilton…

In this note we consider a Landau Hamiltonian perturbed by a random magnetic potential of Anderson type. For a given number of bands, we prove the existence of both strongly localized states at the edges of the spectrum and dynamical…

We review recent results obtained within the framework of the integer quantum Hall effect in the spirit of the work of Germinet, Klein, Schenker in \cite{GKS}. Landau Hamiltonians perturbed by random electric or magnetic perturbations are…

In this note we prove the existence of a localization/delocalization transition for Landau Hamiltonians randomly perturbed by an electric potential with unbounded amplitude. In particular, with probability one, no Landau gaps survive as the…

We perform both analytical and numerical studies of the one-dimensional tight-binding Hamiltonian with stochastic uncorrelated on-site energies and non-fluctuating long-range hopping integrals . It was argued recently [A. Rodriguez at al.,…

We prove quantization of the Hall conductance for continuous ergodic Landau Hamiltonians under a condition on the decay of the Fermi projections. This condition and continuity of the integrated density of states are shown to imply…

We prove the existence of localized states at the edges of the bands for the two-dimensional Landau Hamiltonian with a random potential, of arbitrary disorder, provided that the magnetic field is sufficiently large. The corresponding…

We study a quantum network percolation model which is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We show dynamical localization for parameters corresponding to edges of Landau…

A single model is presented which represents both of the two apparently unrelated localisation problems of the title. The phase diagram of this model is examined using scaling ideas and numerical simulations. It is argued that the…

We consider a two-parameter one-dimensional Hamiltonian with uncorrelated diagonal disorder and {\it non-random} long-range inter-site interaction $J_{mn}=J/|m-n|^{\mu}$. The model is critical at $1<\mu<3/2$ and reveals the…

We show that due to the Landau band mixing the eigenstate localization within the disordered bands get an asymmetric structure: the degree of localization increases in the lower part of the band and decreases in the upper one. The…

We construct a solvable spin chain model of many-body localization (MBL) with a tunable mobility edge. This simple model not only demonstrates analytically the existence of mobility edges in interacting one-dimensional (1D) disordered…

On a flat surface, the Landau operator, or quantum Hall Hamiltonian, has spectrum a discrete set of infinitely degenerate Landau levels. We consider surfaces with asymptotically constant curvature away from a possibly non-compact…

We study many-body localised quantum systems subject to periodic driving. We find that the presence of a mobility edge anywhere in the spectrum is enough to lead to delocalisation for any driving strength and frequency. By contrast, for a…

We say that a quantum spin system is dynamically localized if the time-evolution of local observables satisfies a zero-velocity Lieb-Robinson bound. In terms of this definition we have the following main results: First, for general systems…

Tight-binding 1D random system with long-range correlations is studied numerically using the localisation criterium, which represents the number of sites, covered by the wave function. At low degrees of disorder the signs of a mobility…

In the previous work, we investigated the correlation-induced localization-delocalization transition (LDT) of the wavefunction at band center ($E=0$) in the one-dimensional tight-binding model with fractal disorder [Yamada, EPJB (2015) 88,…

We discuss the problem of localization in two dimensional electron systems in the quantum Hall (single Landau level) regime. After briefly summarizing the well-studied problem of Anderson localization in the non-interacting case, we…

In this paper we study the Landau levels in the non-relativistic dynamics of a neutral particle which possesses a permanent magnetic dipole moment interacting with an external electric field in the curved spacetime background with the…

In one dimension, any disorder is traditionally believed to localize all states. We show that this paradigm breaks down under hyperuniform disorder, which suppresses long-wavelength fluctuations and interpolates between random and periodic…

We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we…