  The cluster perturbation theory (CPT) is one of the simplest but systematic
quantum cluster approaches to lattice models of strongly correlated electrons
with local interactions. By treating the inter-cluster potential, in addition
to the interactions, as a perturbation, it is shown that the CPT can be
reformulated as an all-order re-summation of diagrams within standard
weak-coupling perturbation theory where vertex corrections are neglected. This
reformulation is shown to allow for a straightforward generalization of the CPT
to the general non-equilibrium case using contour-ordered Green's functions.
Solving the resulting generalized CPT equation on the discretized
Keldysh-Matsubara time contour, the transient dynamics of an essentially
arbitrary initial pure or mixed state can be traced. In this way, the
time-dependent expectation values of one-particle observables can be obtained
within an approximation that neglects spatial correlations beyond the extension
of the reference cluster. The necessary computational effort is very moderate.
A detailed discussion and simple test calculations are presented to demonstrate
the strengths and the shortcomings of the proposed approach. The
non-equilibrium CPT is systematic and is controlled in principle by the inverse
cluster size. It interpolates between the non-interacting and the atomic or
decoupled-cluster limit which are recovered exactly and is found to predict the
correct dynamics at very short times in a general non-trivial case. The effects
of initial-state correlations on the subsequent dynamics and the necessity to
extend the Keldysh contour by the imaginary Matsubara branch are analyzed
carefully and demonstrated numerically. It is furthermore shown that the
approach can describe the dissipation of spin and charge to an uncorrelated
bath with an essentially arbitrary number of degrees of freedom.
