Statistical Description of the ComplexBoundaryValue Problem
Abstract
The statistical properties of the parameters of the statistical collision matrix defined in terms of the eigenstates of a complexboundaryvalue problem is studied starting from the Hamiltonian of the system. It is shown that the randommatrix 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 realboundaryvalue problem follow by suitably choosing a parameter.
 Publication:

Physical Review
 Pub Date:
 February 1967
 DOI:
 10.1103/PhysRev.154.891
 Bibcode:
 1967PhRv..154..891U