  We analyze the equilibration process between two either fermionic or bosonic
reservoirs containing ultracold atoms with a fixed total number of particles
that are weakly connected via a few-level quantum system. We allow for both the
temperatures and particle densities of the reservoirs to evolve in time.
Subsequently, linearizing the resulting equations enables us to characterize
the equilibration process and its time scales in terms of equilibrium reservoir
properties and linear-response transport coefficients. Additionally, we
investigate the use of such a device as particle transistor or particle
capacitor and analyze its efficiency.
