Classical versus quantum structure of the scattering probability matrix: Chaotic waveguides

The purely classical counterpart of the scattering probability matrix (SPM) |Sn,m|2 of the quantum scattering matrix S is defined for two-dimensional quantum waveguides for an arbitrary number of propagating modes M. We compare the quantum and classical structures of |Sn,m| 2 for a waveguide with generic Hamiltonian chaos. It is shown that even for a moderate number of channels, knowledge of the classical structure of the SPM allows us to predict the global structure of the quantum one and, hence, understand important quantum transport properties of waveguides in terms of purely classical dynamics. It is also shown that the SPM, being an intensity measure, can give additional dynamical information to that obtained by the Poincare´ maps. © 2002 The American Physical Society.