an:06672996
Zbl 1417.37060
Novaes, Marcel
Energy-dependent correlations in the \(S\)-matrix of chaotic systems
EN
J. Math. Phys. 57, No. 12, 122105, 18 p. (2016).
00362119
2016
j
37A50 37D45 37D50 60B20 81U20 62H20
ballistic cavities; unitary matrix; Weingarten functions
Summary: The \(M\)-dimensional unitary matrix \(S(E)\), which describes scattering of waves, is a strongly fluctuating function of the energy for complex systems such as ballistic cavities, whose geometry induces chaotic ray dynamics. Its statistical behaviour can be expressed by means of correlation functions of the kind \(\left\langle S_{i j}(E + \epsilon) S_{p q}^{\dagger}(E - \epsilon)\right\rangle\), which have been much studied within the random matrix approach. In this work, we consider correlations involving an arbitrary number of matrix elements and express them as infinite series in \(1/M\), whose coefficients are rational functions of \(\epsilon\). From a mathematical point of view, this may be seen as a generalization of the Weingarten functions of circular ensembles.{
\copyright 2016 American Institute of Physics}