Fractional Pumping of Energy into a Ballistic Quantum Ring

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 electromotive force E is much smaller than the level spacing, D. Electron states exponentially localized in energy are found for irrational values of the ratio A ; Dy2eE . Because of relaxation localization does not develop if A is close to a rational number. As a result the accumulated energy as a function of A contains sharp peaks at rational values (fractional pumping). [S0031-9007(97)02728-2] PACS numbers: 73.23.Ad Physical properties of mesoscopic systems are governed by quantum interference. Several phenomena of such a nature have been discussed for systems close to equilibrium. Persistent currents in multiply connected systems [1] as well as universal fluctuations of the conductance are important examples [2]. Coherent dynamics remains crucially important in situations far from equilibrium provided the energy associated with the phase breaking rate is less than the characteristic rate of redistributing electrons in energy space. Consequently, one can expect pronounced mesoscopic behavior even in strongly biased mesoscopic devices, where the dynamics can be effectively tuned by external electric or magnetic fields. In this paper, we consider an example of such a system, namely, a single-channel mesoscopic ring subjected to a nonstationary perpendicular magnetic field, linearly dependent on time. We concentrate on the energy accumulation in such a system. To investigate the role of interference, we take into account electron backscattering from a single potential barrier, embedded in the ring. Tuning the transmission through the barrier by gate potentials one can influence the interference pattern and in this