期刊
ENTROPY
卷 25, 期 1, 页码 -出版社
MDPI
DOI: 10.3390/e25010074
关键词
non-Hermitian random matrices; complex eigenvalues; extreme eigenvalues; eigenvalue outlier; resonances; resonance trapping
Complex eigenvalues of random matrices J = GUE + i(gamma)diag(1,0, ... ,0) provide a simple model for studying resonances in wave scattering from a quantum chaotic system. The eigenvalue density of J undergoes a restructuring at gamma = 1, beyond which a single eigenvalue outlier appears. We describe the scaling with N of the critical region width, resonance positions, resonance widths, and density of extreme eigenvalues in the critical regime.
Complex eigenvalues of random matrices J = GUE + i(gamma)diag(1,0, ... ,0) provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the limit of large matrix dimensions N >> 1 the eigenvalue density of J undergoes an abrupt restructuring at gamma = 1, the critical threshold beyond which a single eigenvalue outlier (broad resonance) appears. We provide a detailed description of this restructuring transition, including the scaling with N of the width of the critical region about the outlier threshold gamma = 1 and the associated scaling for the real parts (resonance positions) and imaginary parts (resonance widths) of the eigenvalues which are farthest away from the real axis. In the critical regime we determine the density of such extreme eigenvalues, and show how the outlier gradually separates itself from the rest of the extreme eigenvalues. Finally, we describe the fluctuations in the height of the eigenvalue outlier for large but finite N in terms of the associated large deviation function.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据