LEVEL-TO-LEVEL FLUCTUATIONS OF THE INVERSE PARTICIPATION RATIO IN FINITE QUASI 1D DISORDERED-SYSTEMS

We study analytically statistics of a quantity known as an inverse par ticipation ratio P which is inversely proportional to a spatial extent of localized eigenfunctions. The fluctuations are found to be crucial ly dependent on the ratio between the system size and mean localizatio n length. As a particular model, we use an ensemble of random banded m atrices which is an equivalent way to describe wires with a large numb er of transverse modes. Our results are in agreement with available nu merical data for periodically driven Hamiltonian systems in the quantu m chaos regime.