Cohen Doron: Quantum stirring of particles in closed devices
We study the quantum analog 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 quantumclassical 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. 


Figure: A scatterer (represented by a black circle) is translated through a systems that has a Fermi occupation of spinless noninteracting electrons. In (a) the system is a simple ring. In (b) it is a chaotic ring (Sinai billiard). In (c) and in (d) we have network systems that are of the same type of (a) and (b) respectively. In (c)(e) the scatterer is a delta function (represented by a big circle), while the current is measured at a section (represented by a dotted vertical line). In (e) we have an open geometry with left and right leads that are attached to reservoirs that have the same chemical potential.  
Additional highlights of the quantum chaos group can be found here 

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