MOMENTS OF WISHART-LAGUERRE AND JACOBI ENSEMBLES OF RANDOM MATRICES: APPLICATION TO THE QUANTUM TRANSPORT PROBLEM IN CHAOTIC CAVITIES
MOMENTS OF WISHART-LAGUERRE AND JACOBI ENSEMBLES OF RANDOM MATRICES: APPLICATION TO THE QUANTUM TRANSPORT PROBLEM IN CHAOTIC CAVITIES
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DOI：
10.5506/aphyspolb.42.1081
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发表时间：
2011-05-01
影响因子：
0.5
通讯作者：
Vivo, Pierpaolo
中科院分区：
文献类型：
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作者：
Livan, Giacomo;Vivo, Pierpaolo
我们收集了具有正交性、酉性和辛对称性的N×N Wishart-Laguerre和Jacobi随机矩阵的实特征值{lambda(I)}的显式和用户友好的表达式。利用这些公式，我们计算了所有对称类的整数矩tau(N)=，而没有任何大的N近似。特别地，我们的结果提供了具有时间反转或自旋翻转对称性的混沌腔中传输本征值的矩的精确表达式，并且在两个输入引线中支持有限和任意数目的电子通道。
We collect explicit and user-friendly expressions for one-point densities of the real eigenvalues {lambda(i)} of N x N Wishart-Laguerre and Jacobi random matrices with orthogonal, unitary and symplectic symmetry. Using these formulae, we compute integer moments tau(n) = for all symmetry classes without any large N approximation. In particular, our results provide exact expressions for moments of transmission eigenvalues in chaotic cavities with time-reversal or spin-flip symmetry and supporting a finite and arbitrary number of electronic channels in the two incoming leads.