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Creators/Authors contains: "Han, Rui"

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  1. ; (, International Mathematics Research Notices)
    Abstract We study discrete magnetic random Schrödinger operators on the square and honeycomb lattice. For the non-random magnetic operator on the hexagonal lattice with any rational magnetic flux, we show that the middle two dispersion surfaces exhibit Dirac cones. We then derive an asymptotic expansion for the density of states on the honeycomb lattice for oscillations of arbitrary rational magnetic flux. This allows us, as a corollary, to rigorously study the quantum Hall effect and conclude dynamical delocalization close to the conical point under disorder. We obtain similar results for the discrete random Schrödinger operator on the $$\mathbb Z^2$$-lattice with weak magnetic fields, close to the bottom and top of its spectrum. 
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  2. ; ; ; (, Journal of Physics A: Mathematical and Theoretical)
    null (Ed.)
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  3. ; ; (, Annales Henri Poincaré)
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  4. ; (, Journal d'Analyse Mathématique)
    Accepted Manuscript Full Text Available
  5. ; ; (, Journal d'Analyse Mathématique)
    Accepted Manuscript Full Text Available
  6. ; (, International Mathematics Research Notices)
    Abstract We consider one-dimensional quasi-periodic Schrödinger operators with analytic potentials. In the positive Lyapunov exponent regime, we prove large deviation estimates, which lead to refined Hölder continuity of the Lyapunov exponents and the integrated density of states, in both small Lyapunov exponent and large coupling regimes. Our results cover all the Diophantine frequencies and some Liouville frequencies. 
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  7. ; (, International mathematics research notices)
    We consider one-dimensional quasi-periodic Schr\"odinger operators with analytic potentials. In the positive Lyapunov exponent regime, we prove large deviation estimates which lead to refined H\"older continuity of the Lyapunov exponents and the integrated density of states, in both small Lyapunov exponent and large coupling regimes. Our results cover all the Diophantine frequencies and some Liouville frequencies. 
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    Accepted Manuscript Full Text Available
  8. ; (, Analysis & PDE)
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  9. ; ; (, Journal of Spectral Theory)
    null (Ed.)
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  10. ; (, Analysis & PDE)
    We establish a version of the fractal uncertainty principle, obtained by Bourgain and Dyatlov in 2016, in higher dimensions. The Fourier support is limited to sets Y⊂ℝd which can be covered by finitely many products of δ-regular sets in one dimension, but relative to arbitrary axes. Our results remain true if Y is distorted by diffeomorphisms. Our method combines the original approach by Bourgain and Dyatlov, in the more quantitative 2017 rendition by Jin and Zhang, with Cartan set techniques. 
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    Accepted Manuscript Full Text Available