  We compare the Landauer, Kubo, and microcanonical [J. Phys. Cond. Matter {\bf
16}, 8025 (2004)] approaches to quantum transport for the average current, the
entanglement entropy and the semiclassical full-counting statistics (FCS). Our
focus is on the applicability of these approaches to isolated quantum systems
such as ultra-cold atoms in engineered optical potentials. For two lattices
connected by a junction, we find that the current and particle number
fluctuations from the microcanonical approach compare well with the values
predicted by the Landauer formalism and FCS assuming a binomial distribution.
However, we demonstrate that well-defined reservoirs (i.e., particles in
Fermi-Dirac distributions) are not present for a substantial duration of the
quasi-steady state. Thus, the Landauer assumption of reservoirs and/or
inelastic effects is not necessary for establishing a quasi-steady state.
Maintaining such a state indefinitely requires an infinite system, and in this
limit well-defined Fermi-Dirac distributions can occur. A Kubo approach -- in
the spirit of the microcanonical picture -- bridges the gap between the two
formalisms, giving explicit analytical expressions for the formation of the
steady state. The microcanonical formalism is designed for closed, finite-size
quantum systems and is thus more suitable for studying particle dynamics in
ultra-cold atoms. Our results highlight both the connection and differences
with more traditional approaches to calculating transport properties in
condensed matter systems, and will help guide the way to their simulations in
cold-atom systems.
