The statistics of eigenvector components of random band matrices: analytical results

Abstract

By using a supersymmetric formalism the authors calculate analytically all higher moments P_q= Sigma _n mod Psi _n mod ^2q generalizing the inverse participation ratio P₂ where Psi _n (1<or=n<or=N) stands for the nth component of an eigenvector of a large random matrix with a band structure. On this basis they reconstruct the whole probability distribution function of eigenvector components. The relation with known numerical results is discussed.