Properties of 1D two-barrier quantum pump with harmonically oscillating   barriers
  We study a one-dimensional quantum pump composed of two oscillating delta-functional barriers. The linear and non-linear regimes are considered. The harmonic signal applied to any or both barriers causes the stationary current. The direction and value of the current depend on the frequency, distance between barriers, value of stationary and oscillating parts of barrier potential and the phase shift between alternating voltages. 
M. M. Mahmoodian, L. S. Braginskii, M. V. Entin