Statistical Description of the Complex-Boundary-Value Problem

Abstract

The statistical properties of the parameters of the statistical collision matrix defined in terms of the eigenstates of a complex-boundary-value problem is studied starting from the Hamiltonian of the system. It is shown that the random-matrix hypothesis can be used to calculate the statistical distribution of quantities such as the complex amplitude. An explicit calculation is carried out for the special case of two dimensions. As a check on the theoretical calculation, it is shown that the results of the real-boundary-value problem follow by suitably choosing a parameter.