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 participation ratio P which is inversely proportional to a spatial extent of localized eigenfunctions. The fluctuations are found to be crucially dependent on the ratio between the system size and mean localization length. As a particular model, we use an ensemble of random banded matrices which is an equivalent way to describe wires with a large number of transverse modes. Our results are in agreement with available numerical data for periodically driven Hamiltonian systems in the quantum chaos regime.