  We propose a theoretical model for the low-frequency noise observed in a
quantum point contact (QPC) electrostatically defined in the 2D electron gas at
a GaAs-AlGaAs interface. In such contacts electron scattering by soft impurity-
or boundary potentials coherently splits an incoming wave function between
different transverse modes. Interference between these modes have been
suggested to explain observed non-linearities in the QPC-conductance. In this
study we invoke the same mechanism and the time-dependent current due to soft
dynamical impurity scattering in order to analyze the low-frequency
(telegraph-like) noise which has been observed along with a nonlinear
conductance. For the simplified case of a channel with two extended (current
carrying) modes, a simple analytical formula for the noise intensity is
derived. Generally we have found qualitative similarities between the noise and
the square of the transconductance. Nevertheless, incidentally there may be
situations when noise is suppressed but transconductance enhanced.
