  A mode-coupling theory for the motion of a strongly forced probe particle in
a dense colloidal suspension is presented. Starting point is the Smoluchowski
equation for $N$ bath and a single probe particle. The probe performs Brownian
motion under the influence of a strong constant and uniform external force
$\Fex$. It is immersed in a dense homogeneous bath of (different) particles
also performing Brownian motion. Fluid and glass states are considered; solvent
flow effects are neglected. Based on a formally exact generalized Green-Kubo
relation, mode coupling approximations are performed and an integration through
transients approach applied. A first-principles theory for the nonlinear
velocity-force relations of the probe particle in a dense fluid and for the
(de-) localized probe in a glass is obtained.
  It extends the mode coupling theory of the glass transition to strongly
forced tracer motion and describes active microrheology experiments. A force
threshold is identified which needs to be overcome to pull the probe particle
free in a glass. For the model of hard sphere particles, the microscopic
equations for the threshold force and the probability density of the localized
probe are solved numerically. Neglecting the spatial structure of the theory, a
schematic model is derived which contains two types of bifurcation, the glass
transition and the force-induced delocalization, and which allows for
analytical and numerical solutions. We discuss its phase diagram, forcing
effects on the time-dependent correlation functions, and the friction
increment. The model was successfully applied to simulations and experiments on
colloidal hard sphere systems [I. Gazuz et. al., Phys. Rev. Lett. 102, 248302
(2009)], while we provide detailed information on its derivation and general
properties.
