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arXiv · 1103.2638

Moments of Wishart-Laguerre and Jacobi ensembles of random matrices: application to the quantum transport problem in chaotic cavities

Giacomo Livan·Pierpaolo Vivo
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Abstract

We collect explicit and user-friendly expressions for one-point densities of the real eigenvalues $\{λ_i\}$ of $N\times N$ Wishart-Laguerre and Jacobi random matrices with orthogonal, unitary and symplectic symmetry. Using these formulae, we compute integer moments $τ_n=<\sum_{i=1}^Nλ_i^n>$ 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.

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Giacomo Livan, Pierpaolo Vivo. 2011-03-16. Moments of Wishart-Laguerre and Jacobi ensembles of random matrices: application to the quantum transport problem in chaotic cavities. https://doi.org/10.5506/aphyspolb.42.1081

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