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Solution of Dyson's equation in a quasi-1D wire

The author obtains the current transmission amplitudes as a function of Fermi energy for electrons scattering from a defect in a quasi-one-dimensional wire by solving Dyson's equation for the single-electron Green function. Dyson's equation in a confined geometry includes both mode conversion and coupling to all the evanescent modes in the wire. After obtaining the Green functions, he uses Fisher and Lee's relationship (1981) between the single-electron Green functions and the current transmission amplitudes through the defect to find all the intersubband and intrasubband transmission probabilities. In agreement with a previous calculation of the transmission amplitudes performed by simply matching wavefunctions at the defect boundary, evanescent modes are shown to dominate the scattering properties whenever the Fermi energy approaches either a new confinement subband or a quasi-bound state splitting off from the higher-lying confinement subbands.