MODE MIXING IN QUANTUM WAVE-GUIDES - A GAUGE FIELD APPROACH

It is shown that the elimination of the discrete transverse motion in a waveguide of arbitrary shape may be described in terms of a non-Abel ian gauge field for the longitudinal dynamics. This allows for an exac t treatment of the scattering between different modes by eliminating t he gauge field at the expense of a non-diagonal matrix of local subban d energies. The method is applied to calculate the local density of st ates (LDOS) in a quantum point contact. Contrary to the total conducta nce which is well described by an adiabatic approximation, mode mixing turns out to play a crucial role for local properties like the LDOS.