Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-03-14
Acta Physica Polonica B vol. 42 (2011) page 1081
Physics
Condensed Matter
Statistical Mechanics
27 pages, 3 figures. Typos fixed, references added
Scientific paper
10.5506/APhysPolB.42.1081
We collect explicit and user-friendly expressions for one-point densities of the real eigenvalues $\{\lambda_i\}$ of $N\times N$ Wishart-Laguerre and Jacobi random matrices with orthogonal, unitary and symplectic symmetry. Using these formulae, we compute integer moments $\tau_n=<\sum_{i=1}^N\lambda_i^n>$ 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.
Livan Giacomo
Vivo Pierpaolo
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