Local density of states and scattering matrix in quasi-one-dimensional systems

Abstract

Mathematical relations between the local density of states (LDOS) and the scattering matrix (i.e., transmission and reflection amplitudes) for quasi-one-dimensional systems are derived in the presence of static uniform magnetic fields. Starting from the definition of the LDOS expressed by the Green's function, we derive the formulas for the LDOS in terms of the functional derivative of the scattering matrix or the Friedel phase with respect to a scattering potential.