Local density of states from transmission amplitudes in multichannel systems

We consider phase-coherent electron transport in the multichannel case with time-reversal symmetry. The two-terminal conduction, as described by the Landauer-Buttiker theory, can be considered to take place in parallel in independent channels: the so-called eigenchannels. We extend the known relationship between the local density of states (LDOS) and phase of the transmission amplitude in one dimension to the multichannel case, and derive a simple explicit expression for the LDOS as a sum of individual eigenchannel contributions. A simple expression for the LDOS that can be used for numerical calculations is given. We show how this formalism can be useful in the description of the electronic states and conductance of metallic nanocontacts.