Quantum synchronization and transresistance quantization in   superconducting devices
  We show theoretically the possibility of quantum synchronization of Josephson and Bloch oscillations in a superconducting device. One needs an $LC$ oscillator to achieve exponentially small rate of synchronization errors. The synchronization leads to quantization of transresistance similar to that in (Fractional) Quantum Hall Effect. 
Alina Hriscu, Yuli V. Nazarov
cond-mat.mes-hall cond-mat.supr-con