Density of States and Lifshitz Tails for Discrete 1D Random Dirac Operators
Density of States and Lifshitz Tails for Discrete 1D Random Dirac Operators
复制标题
离散一维随机狄拉克算子的态密度和 Lifshitz 尾部
DOI：
10.1007/s11040-021-09403-4
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
E. C. de Oliveira
中科院分区：
文献类型：
--
作者：
R. Prado;C. R. de Oliveira;E. C. de Oliveira
本文研究了一维格点上一类随机Dirac算符的态密度和Lifshitz尾。这些算子由一个离散的自由狄拉克算子与一个随机势的和组成。势是由两个不同的标量势形成的对角矩阵，这两个标量势是独立同分布的随机变量序列，根据紧支撑的Borel概率测度。用有限体积量的两种方法证明了这些狄拉克算符的态密度测度的存在性。通过使用这些方法之一，我们表明，态密度的分布函数指数衰减的能量附近的谱带边缘，即，我们为这些算子建立了Lifshitz尾。Lifshitz尾首先建立狄拉克运营商限制到适当的子空间的能量，并利用这一点，扩展到全运营商，包括发生的内部尾巴的情况下，频谱间隙。
We study the density of states and Lifshitz tails for a family of random Dirac operators on the one-dimensional lattice. These operators consist of the sum of a discrete free Dirac operator with a random potential. The potential is a diagonal matrix formed by two different scalar potentials, which are sequences of independent and identically distributed random variables according to a Borel probability measure of compact support in. The existence of the density of state measure for these Dirac operators is obtained through two approaches by finite-volume quantities. By using one of these approaches, we show that the distribution function of the density of states decays exponentially for energies near the spectral band edges, i.e., we establish Lifshitz tails for these operators. Lifshitz tails are established first for Dirac operators restricted to appropriate subspaces of energies and, using this, extended to the full operators, including the occurrence of internal tails in the case of spectral gap.