The spinless Falicov-Kimball model exhibits outside the particle-hole symmetric point different stable nonhomogeneous charge orderings. These include the well known charge stripes and a variety of orderings with phase separated domains, which can significantly influence the charge transport through the correlated electron system. We show this by investigating a heterostructure, where the Falicov-Kimball model on a finite two-dimensional lattice is located between two non-interacting semi-infinite leads. We use a combination of nonequilibrium Green's functions techniques with a signproblem-free Monte Carlo method for finite temperatures or simulated annealing technique for the ground state to address steady-state transport through the system. We show that different groundstate phases of the central system can lead to simple metallic-like or insulating charge transport characteristics, but also to more complicated current-voltage dependencies reflecting a multi-band character of the transmission function. Interestingly, with increasing temperature, the orderings tend to form transient phases before the system reaches the disordered phase. This leads to nontrivial temperature dependencies of transmission function and charge current.

We investigate nonequilibrium processes in magnetic nano-junctions employing a numerical approach, which combines classical spin dynamics with the hierarchical equations of motion technique for the quantum dynamics of the conduction electrons. Focusing on the spin dynamics, we find that the spin relaxation rates depend in a non-monotonous way on the coupling between the localized spin and conduction electrons, with a pronounced maximum at intermediate coupling strength. This result can be understood by analyzing the local density of states. In the case of a magnetic junction subject to an external dc-voltage, spin relaxation exhibits resonant features reflecting the electronic spectrum of the system. In addition, in multi-site junctions, spin relaxation is also influenced by electron localization.

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We utilize a hybrid quantum-classical equation of motion approach to investigate the spin dynamics and spin-transfer torque in a spin valve under bias voltage. We show that the interplay between localized classical magnetic moments and conduction electrons induces a complex effective exchange coupling between the magnetic layers. This leads to a declination of magnetizations from layer anisotropy axes even in equilibrium. Introducing a finite bias voltage triggers spin currents and related spin transfer torques which further tilt the magnetizations and govern the relaxation processes of the spin dynamics. Analyzing different scenarios of the applied bias voltage, we show that symmetric and asymmetric voltage drops can lead to relaxation times of the spin dynamics that differ by several orders of magnitude at comparable charge currents. In both cases we observe resonant features, where the relaxation is boosted whenever the chemical potential of the leads matches the maxima in the density of the states of the spin-valve electrons.