We have opened a new field of study which we call "quantum stirring": we ask what is the DC current which is induced (say) in a ring due to AC modulation of the potential. (It is like "quantum pumping" but in a closed geometry).
 
Some surprising effects are revealed, e.g. the counter stirring effect: by operating a pump in a closed circuit we can get a current in the opposite direction due to interference effect.
 
On the formal aspect we have introduced the "splitting ratio" concept that allows to bypass the heavy machinery of the Kubo formalism that I had promoted in past studies. Current research activity concerns the statistic of circulating currents in large network.
 
Additionally we have introduced a new direction in the study of counting statistics, regarding the induced currents in closed devices with multiple path geometries and in quantum stirring problems. This is quite different from the traditional analysis of shot noise in open geometries. For example: the partitioning of current turns out to be a noiseless process in the adiabatic limit (hence we use the term splitting); while the fluctuations due to the non-adiabaticity of the driving [e.g. in a sequence of several Landau-Zener transitions of a pumping cycle] have an interference "addition law" which is not the same as in the calculation of transition probabilities.
 
Review: Quantum transport and counting statistics in closed systems [arXiv] [pdf], (Prague, 2008).