论文标题
某些随机统一矩阵的水平可压缩性
Level compressibility of certain random unitary matrices
论文作者
论文摘要
原点处光谱形式的值（称为水平可压缩性）是随机光谱的重要特征。该论文专门针对该数量的分析计算，用于描述具有中间光谱统计模型的不同随机单位矩阵。这些计算基于G. Tanner在[J.物理。答：数学。 Cen. 34，8485（2001）用于混沌系统。该方法的主要成分是确定过渡矩阵的特征值，其矩阵元素等于初始单位矩阵的基质元素的平方模量。本文的主要结果是证明了从屏障台球的确切量化和屏障台球本身的确切定量得出的随机统一矩阵的水平可压缩性，无论障碍的高度和位置如何，等于$ 1/2 $。
The value of spectral form factor at the origin, called level compressibility, is an important characteristic of random spectra. The paper is devoted to analytical calculations of this quantity for different random unitary matrices describing models with intermediate spectral statistics. The computations are based on the approach developed by G. Tanner in [J. Phys. A: Math. Gen. 34, 8485 (2001)] for chaotic systems. The main ingredient of the method is the determination of eigenvalues of a transition matrix whose matrix elements equal squared moduli of matrix elements of the initial unitary matrix. The principal result of the paper is the proof that the level compressibility of random unitary matrices derived from the exact quantisation of barrier billiards and consequently of barrier billiards themselves is equal to $1/2$ irrespectively of the height and the position of the barrier.
