Non-Hermitian random matrix models: Free random variable approach

被引：71
|
作者：
Janik, RA
Nowak, MA
Papp, G
Wambach, J
Zahed, I
机构：
[1] GSI DARMSTADT, D-64291 DARMSTADT, GERMANY
[2] TH DARMSTADT, INST KERNPHYS, D-6100 DARMSTADT, GERMANY
[3] EOTVOS LORAND UNIV, INST THEORET PHYS, BUDAPEST, HUNGARY
[4] SUNY STONY BROOK, DEPT PHYS, STONY BROOK, NY 11794 USA
来源：
PHYSICAL REVIEW E | 1997年 / 55卷 / 04期
关键词：
D O I：
10.1103/PhysRevE.55.4100
中图分类号：
O35 [流体力学]; O53 [等离子体物理学];
学科分类号：
070204 ; 080103 ; 080704 ;
摘要：
Using the standard concepts of free random variables, we show that for a large class of non-Hermitian random matrix models, the support of the eigenvalue distribution follows from their Hermitian analogs using a conformal transformation. We also extend the concepts of free random variables to the class of non-Hermitian matrices, and apply them to the models discussed by Ginibre-Girko (elliptic ensemble) [J. Ginibre, J. Math. Phys. 6, 1440 (1965); V. L. Girko, Spectral Theory of Random Matrices (in Russian) (Nauka, Moscow, 1988)] and Mahaux-Weidenmuller (chaotic resonance scattering) [C. Mahaux and H. A. Weidenmuller, Shell-model Approach to Nuclear Reactions (North-Holland, Amsterdam, 1969)].
引用
收藏
页码：4100 / 4106
页数：7
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