Intermediate statistics of the quasi-energy spectrum and quantum localisation of classical chaos

The statistical properties of the quasi-energy spectrum in a simple quantum model are investigated for the case when the corresponding classical system is fully chaotic while quantum chaos is restricted by the localisation effects. It is shown that the level spacing distribution depends effectively on some parameter which is the ratio of the dimension of the eigenfunctions (mean localisation length) to the total number of the quasi-energy levels. Numerical data for a wide range of parameters of the system are given.