Exact-dimensional property of density of states measure of Sturm Hamiltonian
作者： Yanhui Qu
DOI:
关键词: Mathematics 、 Lambda 、 Density of states 、 Bounded type 、 Mathematical physics 、 Hamiltonian (quantum mechanics) 、 Mathematical analysis
摘要: For frequency $\alpha$ of bounded type and coupling $\lambda>20$, we show that the density states measure $\NN_{\alpha,\lambda}$ related Sturm Hamiltonian is exact upper lower dimensional, however, in general it not exact-dimensional.
arxiv.org参考文章(18)
Jeffrey Shallit, Jean-Paul Allouche, Automatic Sequences: Theory, Applications, Generalizations ,(2003)
Paul Munger, Frequency dependence of H\"older continuity for quasiperiodic Schr\"odinger operators arXiv: Mathematical Physics. ,(2013)
Jihua Ma, Hui Rao, Zhiying Wen, Dimensions of cookie-cutter-like sets Science China-mathematics. ,vol. 44, pp. 1400- 1412 ,(2001) , 10.1007/BF02877068
M. Lothaire, Algebraic Combinatorics on Words ,(2002)
Pertti Mattila, Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability ,(1995)
Mahito Kohmoto, Leo P. Kadanoff, Chao Tang, Localization Problem in One Dimension: Mapping and Escape Physical Review Letters. ,vol. 50, pp. 1870- 1872 ,(1983) , 10.1103/PHYSREVLETT.50.1870
David Damanik, Anton Gorodetski, THE DENSITY OF STATES MEASURE OF THE WEAKLY COUPLED FIBONACCI HAMILTONIAN Geometric and Functional Analysis. ,vol. 22, pp. 976- 989 ,(2012) , 10.1007/S00039-012-0173-8
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
MARC KESSEBHMER, BERND O. STRATMANN, A multifractal formalism for growth rates and applications to geometrically finite Kleinian groups Ergodic Theory and Dynamical Systems. ,vol. 24, pp. 141- 170 ,(2004) , 10.1017/S0143385703000282
DIMITRIOS GATZOURAS, YUVAL PERES, Invariant measures of full dimension for some expanding maps Ergodic Theory and Dynamical Systems. ,vol. 17, pp. 147- 167 ,(1997) , 10.1017/S0143385797060987