Bound-state evolution in curved waveguides and quantum wires

A theoretical study of a waveguide with a uniformly curved section is presented within the envelope function approximation. Utilizing analytical solutions in each part of the waveguide, exact expression of the scattering matrix of the system is derived. Based on it, a conductance of the waveguide is calculated for the wide range of the bend angle and radius. It is shown that a quasibound state formed as a result of the bend, at some critical parameters of the curve becomes a true bound state with infinite lifetime. It has its degenerate continuum counterpart, but does not interact with it. As a result of a constructive resonant interference in the bend, dip in the conductance, which is an essential property for the noncritical values, vanishes with full transmission being observable instead. Mathematical and physical interpretation of these results is given, and characteristic features of the critical parameters are discussed. Comparison with quantum waveguides with other types of nonuniformity is performed.