  Using a supersymmetry formalism, we reduce exactly the problem of electron
motion in an external potential to a new supermatrix model valid at all
distances. All approximate nonlinear sigma models obtained previously for
disordered systems can be derived from our exact model using a coarse-graining
procedure. As an example, we consider a model for a smooth disorder and
demonstrate that using our approach does not lead to a 'mode-locking' problem.
As a new application, we consider scattering on strong impurities for which the
Born approximation cannot be used. Our method provides a new calculational
scheme for disordered and chaotic systems.
