Analytical derivation of the scaling law for the inverse participation ratio in quasi-one-dimensional disordered systems

We present a calculation of the inverse participation ratio in finite quasi-one-dimensional samples in the whole range of the scaling parameter within the framework of a one-dimensional nonlinear supermatrix {σ} model. The results are valid for both thick wires and random band matrices with large bandwidth and so are relevant for quantum chaos problems. The derived form of the scaling law exactly coincides with the empirical expression deduced earlier from results of computer simulations.