Quantum stirring of particles in closed devices

We study the quantum analogue of stirring of water inside a cup using a spoon. This can be regarded as a prototype example for quantum pumping in closed devices. The current in the device is induced by translating a scatterer. Its calculation is done using the Kubo formula approach. The transported charge is expressed as a line integral that encircles chains of Dirac monopoles. For simple systems, the results turn out to be counter-intuitive, e.g. as we move a small scatterer 'forward' the current is induced 'backwards'. One should realize that the route towards quantum-classical correspondence has to do with 'quantum chaos' considerations, and hence assumes greater complexity of the device. We also point out the relation to the familiar S-matrix formalism which is used to analyse quantum pumping in open geometries.