  The nonequilibrium dynamics of correlated many-particle systems is of
interest in connection with pump-probe experiments on molecular systems and
solids, as well as theoretical investigations of transport properties and
relaxation processes. Nonequilibrium Green's functions are a powerful tool to
study interaction effects in quantum many-particle systems out of equilibrium,
and to extract physically relevant information for the interpretation of
experiments. We present the open-source software package NESSi (The
Non-Equilibrium Systems Simulation package) which allows to perform many-body
dynamics simulations based on Green's functions on the L-shaped Kadanoff-Baym
contour. NESSi contains the library libcntr which implements tools for basic
operations on these nonequilibrium Green's functions, for constructing Feynman
diagrams, and for the solution of integral and integro-differential equations
involving contour Green's functions. The library employs a discretization of
the Kadanoff-Baym contour into time $N$ points and a high-order implementation
of integration routines. The total integrated error scales up to
$\mathcal{O}(N^{-7})$, which is important since the numerical effort increases
at least cubically with the simulation time. A distributed-memory
parallelization over reciprocal space allows large-scale simulations of lattice
systems. We provide a collection of example programs ranging from dynamics in
simple two-level systems to problems relevant in contemporary condensed matter
physics, including Hubbard clusters and Hubbard or Holstein lattice models. The
libcntr library is the basis of a follow-up software package for nonequilibrium
dynamical mean-field theory calculations based on strong-coupling perturbative
impurity solvers.
