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 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.
||Figure: A scatterer (represented by a black circle) is translated through a systems that has a Fermi occupation of spinless non-interacting 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