动力猝灭随机矩阵与同列间隙
Dynamical and Quenched Random Matrices and Homolumo Gap
摘要：
我们考虑一种相当一般的矩阵模型，其中矩阵M表示玻色子系统与单个费米子相互作用的哈密顿量。矩阵的涨落部分是由一些基本的随机性和部分动态，甚至量子力学。然后，我们研究了homolumo-gap效应，这意味着我们研究了单费米子哈密顿矩阵M的能级密度如何在费米面附近衰减。在淬火的随机性（基本的）占主导地位的量子力学的情况下，我们表明，在第一近似的homolumo间隙的特点是没有单费米子水平之间的两个陡峭的间隙边界。在第一种近似中，充满和空的能级密度被推到了一边。在下一个近似中，谱密度中的这些陡峭下降被涂抹掉以具有误差函数形状。所研究的模型可以被认为是更一般的情况下，考虑整个领域的矩阵-定义在一些相空间-而不是一个单一的矩阵的第一步。
英文摘要：
We consider a rather general type of matrix model, where the matrix M represents a Hamiltonian of the interaction of a bosonic system with a single fermion. The fluctuations of the matrix are partly given by some fundamental randomness and partly dynamically, even quantum mechanically. We then study the homolumo-gap effect, which means that we study how the level density for the single-fermion Hamiltonian matrix M gets attenuated near the Fermi surface. In the case of the quenched randomness (the fundamental one) dominating the quantum mechanical one we show that in the first approximation the homolumo gap is characterized by the absence of single-fermion levels between two steep gap boundaries. The filled and empty level densities are in this first approximation just pushed, each to its side. In the next approximation these steep drops in the spectral density are smeared out to have an error-function shape. The studied model could be considered as a first step towards the more general case of considering a whole field of matrices - defined say on some phase space - rather than a single matrix.
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