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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer Berlin Heidelberg

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DOI

10.1007/bf01923556

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1432-0916

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Singular Continuous Spectrum for Singular Potentia

Authors: Svetlana Jitomirskaya Fan Yang
Publish Date: 2017/01/17
Volume: 351, Issue: 3, Pages: 1127-1135
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Abstract

We prove that Schrödinger operators with meromorphic potentials H alphathetau n=u n+1+u n1+ fracgtheta+nalphaftheta+nalpha u n have purely singular continuous spectrum on the set E LE deltaalpha theta where delta is an explicit function and L is the Lyapunov exponent This extends results of Jitomirskaya and Liu Arithmetic spectral transitions for the Maryland model CPAM to appear for the Maryland model and of AvilaYou and Zhou Sharp Phase transitions for the almost Mathieu operator Preprint 2015 for the almost Mathieu operator to the general family of meromorphic potentials

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  2. Hausdorff Dimension of Julia Sets of Feigenbaum Polynomials with High Criticality
  3. Stability and Duality in $${\mathcal{N}\,{=}\,2}$$ Supergravity
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  5. Binding of Polarons and Atoms at Threshold
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  7. On Perturbations of the Schwarzschild Anti-De Sitter Spaces of Positive Mass
  8. Wall-Crossing, Free Fermions and Crystal Melting
  9. Standing Ring Blow up Solutions to the N-Dimensional Quintic Nonlinear Schrödinger Equation
  10. Laminar Boundary Layers in Convective Heat Transport
  11. There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group
  12. Duality of 2D Gravity as a Local Fourier Duality
  13. Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem with Degenerate Density Dependent Viscosities
  14. Extended Scaling Relations for Planar Lattice Models
  15. Infinite-Dimensional Schur–Weyl Duality and the Coxeter–Laplace Operator
  16. Phase Boundaries in Algebraic Conformal QFT
  17. On the Singularity of the Free Energy at a First Order Phase Transition
  18. Free Analog of Pressure and Its Legendre Transform
  19. Continuity of the Lyapunov Exponents for Quasiperiodic Cocycles
  20. On the Correlation Function of the Characteristic Polynomials of the Hermitian Wigner Ensemble
  21. Stationary Random Metrics on Hierarchical Graphs Via $${(\min,+)}$$-type Recursive Distributional Equations
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  27. A Monoidal Category for Perturbed Defects in Conformal Field Theory
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  30. High Energy Limits of Laplace-Type and Dirac-Type EigenFunctions and Frame Flows
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