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.
Cite
@article{arxiv.1208.1038,
title = {Quantum synchronization and transresistance quantization in superconducting devices},
author = {Alina Hriscu and Yuli V. Nazarov},
journal= {arXiv preprint arXiv:1208.1038},
year = {2013}
}