Frequency dependence of H\"older continuity for quasiperiodic Schr\"odinger operators

作者: Paul Munger

DOI:

关键词:

摘要: We prove estimates on the H\"older exponent of density states measure for discrete Schr\"odinger operators with potential form $V(n) = \lambda(\lfloor(n+1)\beta\rfloor - \lfloor n\beta\rfloor)$, $\lambda$ large enough, and conclude that almost all values $\beta$, is not continuous.

参考文章(7)
D. Shechtman, I. Blech, D. Gratias, J. W. Cahn, Metallic Phase with Long-Range Orientational Order and No Translational Symmetry Physical Review Letters. ,vol. 53, pp. 1951- 1953 ,(1984) , 10.1103/PHYSREVLETT.53.1951
Serguei Tcheremchantsev, David Damanik, Mark Embree, Anton Gorodetski, The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian Communications in Mathematical Physics. ,vol. 280, pp. 499- 516 ,(2008) , 10.1007/S00220-008-0451-3
J. Bellissard, B. Iochum, E. Scoppola, D. Testard, Spectral properties of one-dimensional quasi-crystals Communications in Mathematical Physics. ,vol. 125, pp. 527- 543 ,(1989) , 10.1007/BF01218415
David Damanik, Anton Gorodetski, Spectral and Quantum Dynamical Properties of the Weakly Coupled Fibonacci Hamiltonian Communications in Mathematical Physics. ,vol. 305, pp. 221- 277 ,(2011) , 10.1007/S00220-011-1220-2
Qing-Hui Liu, Yan-Hui Qu, Zhi-Ying Wen, The fractal dimensions of the spectrum of Sturm Hamiltonian Advances in Mathematics. ,vol. 257, pp. 285- 336 ,(2014) , 10.1016/J.AIM.2014.02.019
Aleksandr Ja Chinčin, Continued Fractions ,(1964)
David Damanik, Anton Gorodetski, Hölder Continuity of the Integrated Density of States for the Fibonacci Hamiltonian Communications in Mathematical Physics. ,vol. 323, pp. 497- 515 ,(2013) , 10.1007/S00220-013-1753-7