细节中的魔鬼：离散Preisach记忆模型的谱和特征值分布
The Devil is in the Details: Spectrum and Eigenvalue Distribution of the Discrete Preisach Memory Model
摘要：
我们考虑与描述离散Preisach记忆模型的$2^{N}$状态之间的转换的图相关联的邻接矩阵。该矩阵还可以与后进先出库存管理规则关联。我们提出了一个明确的解决方案的频谱显示的特征多项式是产品的切比雪夫多项式。的本征值分布（态密度）明确计算，并示出接近缩放魔鬼的楼梯。邻接矩阵的特征向量也被解析表示。
英文摘要：
We consider the adjacency matrix associated with a graph that describes transitions between $2^{N}$ states of the discrete Preisach memory model. This matrix can also be associated with the last-in-first-out inventory management rule. We present an explicit solution for the spectrum by showing that the characteristic polynomial is the product of Chebyshev polynomials. The eigenvalue distribution (density of states) is explicitly calculated and is shown to approach a scaled Devil's staircase. The eigenvectors of the adjacency matrix are also expressed analytically.
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