Sharp phase transitions for the almost Mathieu operator
Sharp phase transitions for the almost Mathieu operator
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DOI：
10.1215/00127094-2017-0013
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发表时间：
2015-12
影响因子：
2.5
通讯作者：
A. Avila;J. You;Qi Zhou
中科院分区：
文献类型：
--
作者：
A. Avila;J. You;Qi Zhou
众所周知，几乎马蒂厄算子的谱类型从根本上取决于耦合常数的强度和频率的算术特性。我们研究了这些因素之间的竞争，并找到了从奇异连续谱到纯点谱的相变发生点，这解决了Jitomirskaya在\cite{Ji95,J07}中的猜想。与 \cite{Aab} 一起，我们给出了几乎 Mathieu 算子的相变的清晰描述。
It is known that the spectral type of the almost Mathieu operator depends in a fundamental way on both the strength of the coupling constant and the arithmetic properties of the frequency. We study the competition between those factors and locate the point where the phase transition from singular continuous spectrum to pure point spectrum takes place, which solves Jitomirskaya's conjecture in \cite{Ji95,J07}. Together with \cite{Aab}, we give the sharp description of phase transitions for the almost Mathieu operator.