Symmetry and transport of waves in one-dimensional disordered systems

The transfer matrix approach to transport in one-dimensional systems is reviewed in detail with emphasis on the role of symmetrized products. First, the concept of a transfer matrix is introduced, and then generalized through the introduction of symmetrized products. The resulting formalism is successively applied to the problem of averaging: resistance, density of states, conductance (i.e. transmission coefficient), phases of transmission and reflection, and frequency response. Finally the problem of 1/f noise in disordered systems is addressed in the language of symmetrized transfer matrices.