Relation between Anderson- and Invariant Imbedding Models for Transport in Finite Chains and Study of Phase- and Delay Time Distributions for Strong Disorder

The invariant imbedding evolution equations for the amplitude reflection and transmission coefficients of a disordered 1D chain are shown to follow from the continuum limit, for weak disorder, of recursion relations between reflection (transmission) coefficients of Anderson chains of N and N-1 atoms embedded in infinite non-disordered chains. We show that various available analytical and numerical results for reflection phase distributions in the Anderson- and invariant imbedding models are in good qualitative agreement, as expected from the above equivalence of these models. We also discuss the distribution of reflection phases and of reflection delay times for an Anderson model with a simple distribution of on-site potentials characterizing extreme strong disorder.