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We systematically study the first three terms in the asymptotic expansions of the moments of the transmission eigenvalues and proper delay times as the number of quantum channels n in the leads goes to infinity. The computations are based on the assumption that the Landauer-Büttiker scattering matrix for chaotic ballistic cavities can be modelled by the circular ensembles of random matrix theory. The starting points are the finite-n formulae that we recently discovered [F. Mezzadri and N. J. Simm, 'Moments of the transmission eigenvalues, proper delay times and random matrix theory,' J. Math. Phys. 52, 103511 (2011)]. Our analysis includes all the symmetry classes β ∈ {1, 2, 4}; in addition, it applies to the transmission eigenvalues of Andreev billiards, whose symmetry classes were classified by Zirnbauer ['Riemannian symmetric superspaces and their origin in random-matrix theory,' J. Math. Phys. 37(10), 4986 (1996)] and Altland and Zirnbauer ['Random matrix theory of a chaotic Andreev quantum dot,' Phys. Rev. Lett. 76(18), 3420 (1996); and 'Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures,' Phys. Rev. B 55(2), 1142 (1997)]. Where applicable, our results are in complete agreement with the semiclassical theory of mesoscopic systems developed by Berkolaiko et al. ['Full counting statistics of chaotic cavities from classical action correlations,' J. Phys. A: Math. Theor. 41(36), 365102 (2008)] and Berkolaiko and Kuipers ['Moments of the Wigner delay times,' J. Phys. A: Math. Theor. 43(3), 035101 (2010); and 'Transport moments beyond the leading order,' New J. Phys. 13(6), 063020 (2011)]. Our approach also applies to the Selberg-like integrals. We calculate the first two terms in their asymptotic expansion explicitly. [ABSTRACT FROM AUTHOR]

We develop a method to compute the moments of the eigenvalue densities of matrices in the Gaussian, Laguerre, and Jacobi ensembles for all the symmetry classes β ∈ {1, 2, 4} and finite matrix dimension n. The moments of the Jacobi ensembles have a physical interpretation as the moments of the transmission eigenvalues of an electron through a quantum dot with chaotic dynamics. For the Laguerre ensemble we also evaluate the finite n negative moments. Physically, they correspond to the moments of the proper delay times, which are the eigenvalues of the Wigner-Smith matrix. Our formulae are well suited to an asymptotic analysis as n → ∞. [ABSTRACT FROM AUTHOR]

Inserting both polar A and magnetic B ions in a same crystalline phase, such as A = Bi3+, B = Fe3+ or Mn3+ in simple perovskites ABO3, has been successful in achieving multiferroic properties with large ferroelectric and magnetic orders. However, modest magnetoelectric couplings have been hitherto reported, thus preventing any application for future electronics. By means of neutron diffraction, we found a large uniform C-type modulation of an E-type antiferromagnetic structure of the Mn3+ ions in the quadruple perovskite BiMn3Mn4O12. A symmetry analysis indicates that this modulation is induced by the internal strain created by the polar Bi3+ ion, which gives evidence of a large magnetoelectric coupling driven by inverse magnetostriction. This modulation is indeed absent in the isomorphic and isovalent compound LaMn3Mn4O12 containing the nonpolar La3+ ion. Our analysis indicates that this coupling mechanism is effective owing to the symmetry-limited structural distortions and inhomogeneities characteristic of the quadruple perovskite structure, thus preventing the release of the strain. We conclude that internal strain is a key control parameter to achieve large magnetoelectric couplings in proper ferroelectrics. [ABSTRACT FROM AUTHOR]