Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1997-01-17
Phys. Rev. Lett. 78, 2196 (1997)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
4 pages, LaTex (RevTeX), 2 figures in eps-format, to appear in Physical Review Letters
Scientific paper
10.1103/PhysRevLett.78.2196
We consider the energy stored in a one-dimensional ballistic ring with a barrier subject to a linearly time-dependent magnetic flux. An exact analytic solution for the quantum dynamics of electrons in the ring is found for the case when the electro-motive force ${\cal E}$ is much smaller than the level spacing, $\Delta$. Electron states exponentially localized in energy are found for irrational values of the ratio $A\equiv\Delta/2e{\cal E}$. Relaxation limits the dynamic evolution and localization does not develop if $A$ is sufficiently close to a rational number. As a result the accumulated energy becomes a regular function of $A$ containing a set of sharp peaks at rational values (fractional pumping). The shape of the peaks and the distances between them are governed by the interplay between the strength of backscattering and the relaxation rate.
Galperin Yu.
Gorelik L.
Jonson Mats
Kulinich S.
Shekhter Robert I.
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