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

Abstract

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.

27 pages, 3 figures. Typos fixed, references added

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Cited by in corpus (22)

• Random pure states: quantifying bipartite entanglement beyond the linear statistics
• Moments of the transmission eigenvalues, proper delay times and random matrix theory I
• Tau-Function Theory of Quantum Chaotic Transport with beta=1,2,4
• Moments of the transmission eigenvalues, proper delay times and random matrix theory II
• Universality in chaotic quantum transport: The concordance between random matrix and semiclassical theories
• Efficient semiclassical approach for time delays
• Moments of random matrices and hypergeometric orthogonal polynomials
• Combinatorial theory of the semiclassical evaluation of transport moments I: Equivalence with the random matrix approach
• Large $N$ expansions for the Laguerre and Jacobi $\beta$ ensembles from the loop equations
• Moments of the eigenvalue densities and of the secular coefficients of $\beta$-ensembles
• Large deviation eigenvalue density for the soft edge Laguerre and Jacobi $\beta$-ensembles
• Transport moments and Andreev billiards with tunnel barriers
• Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions
• Spectral Properties of the Jacobi Ensembles via the Coulomb Gas approach
• Linear Differential Equations for the Resolvents of the Classical Matrix Ensembles
• Joint statistics of quantum transport in chaotic cavities
• Semiclassical treatment of quantum chaotic transport with a tunnel barrier
• Statistics of quantum transport in weakly non-ideal chaotic cavities
• Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix
• Expanding the reach of quantum optimization with fermionic embeddings
• Matrix models for extremal and integrated correlators of higher rank
• Optimization landscape in the simplest constrained random least-square problem