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Quantum stirring of particles in closed devices

Gilad Rosenberg·Doron Cohen
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Abstract

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 analyze quantum pumping in open geometries.

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Gilad Rosenberg, Doron Cohen. 2006-01-11. Quantum stirring of particles in closed devices. https://doi.org/10.1088/0305-4470%2F39%2F10%2F004

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