  In the thesis we present an analytic approach towards exact description for
steady state density operators of nonequilibrium quantum dynamics in the
framework of open systems. We employ the so-called quantum Markovian semi-group
evolution, i.e. a general form of time-autonomous positivity and
trace-preserving dynamical equation for reduced density operators, by only
allowing unitarity-breaking dissipative terms acting at the boundaries of a
system. Such setup enables to simulate macroscopic reservoirs for different
values of effective thermodynamic potentials, causing incoherent transitions
between quantum states which are modeled with aid of the Lindblad operators.
This serves as a simple minimalistic model for studying quantum transport
properties, either in the linear response domain or in more general regimes far
from canonical equilibrium. We are mainly exploring possibilities of
identifying nonequilibrium situations which are amenable to exact description
within matrix product state representation, by exclusively focusing on steady
states, i.e. fixed points of the Lindblad equation, of certain prototypic
interacting integrable spin chains driven by incoherent polarizing processes.
Finally, we define a concept of pseudo-local extensive almost-conserved
quantities by allowing a violation of time-invariance up to boundary-localized
terms. We elucidate the role of such quantities on non-ergodic behaviour of
temporal correlation functions rendering anomalous transport properties. It
turns out that such conservation laws can be generated by means of boundary
universal quantum transfer operators of the fundamental integrable models.
