Quasi-one-dimensional random systems: weak-disorder expansion of Lyapunov exponents

Abstract

The author constructs a nondegenerate weak-disorder expansion of Lyapunov exponents of quasi-one-dimensional random systems Md* infinity , and for both diagonal and off-diagonal disorders. The supersymmetric representation of the Green function enables him to express the coefficients of expansion graphically. For diagonal disorder, and explicit form of expansion up to fourth order in disorder is given. Inside the energy band, there are critical energies for which the expansion does not work. He did not succeed in generalising the expansion for the degenerate case.