  A great variety of experiments, like heat release measurements, acoustic
measurements, and transport measurements on mesoscopic samples have proved that
two level systems (TLSs) have a crucial role in the low temperature thermal and
electric properties of disordered systems. This paper is aimed at reviewing the
role of slow TLSs in point contacts. First the theory of point contacts is
summarized, concentrating on the discussion of different point contact models,
and on the different regimes of electron flow in the contact, mainly focusing
on the ballistic and diffusive limit. The Boltzmann equation is solved in both
regimes, and the position dependence of the electrical potential is determined.
Then the scattering processes in point contacts are investigated, particularly
concentrating on the scattering on slow TLSs. If the the electron assisted
transitions between the two states are negligible the electron-two level system
interaction can be treated with a simplified Hamiltonian. The scattering on
such slow TLSs causes nonlinearity in the current-voltage characteristics of
the point contact, which can be determined using Fermi's golden role. These
calculations are presented showing both the contribution of elastic and
inelastic scattering, and including the dependence on the position of the TLS,
and on the effect of high frequency irradiation. These results are used to
discuss the differences between these slow TLSs and the fast centers which may
be described by the two channel Kondo model. The available experimental results
are analyzed, distinguishing between the effects due to the different types of
TLSs.
