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 one-dimensional 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 imbedded in infinite nondisordered chains. As an illustration of the equivalence of the invariant-imbedding equations and the Anderson model for a weak disorder, we show that various available analytical and numerical results for reflection-phase distributions for these models are in good qualitative agreement. 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.