Theory of non-linear transport in quantum waveguides

The equations for quantum ballistic transport in inhomogeneous quantum wire structures are transformed into a set of one-dimensional coupled mode equations where the coupling parameters are explicitly dependent on the shape parameters for the confinement potential. In the adiabatic approximation or in the extreme quantum limit the resulting motion is governed by an effective Hamiltonian which contains the influence of quasi-electric fields and quasi-momentum dependent forces which arise from the inhomogeneous shape parameter variation along the quantum waveguide. The subsequent transport may be described by a Boltzmann-like kinetic equation and hot-electron effects arising from variations in the waveguide profile are predicted. It is shown that transport through a wide region of an otherwise narrow wire leads to multiply-connected electron paths which will produce Aharonov-Bohm resonances. The analytical formalism is underpinned by a new numerical method suitable for 3-D studies based on representing the inhomogeneous waveguide by an equivalent network of one-dimensional wires.