Quantum phase diffusion in ac-driven superconducting atomic point   contacts
  The impact of quantum fluctuations on the phase diffusion in resistively shunted superconducting quantum points subject to an external ac-voltage is studied. Based on an extension of the classical Smoluchowski equation to the quantum regime, numerical results for fractional and integer Shapiro resonances are investigated to reveal characteristic features of quantum effects. It is shown that typically in the quantum regime the broadening of resonances cannot be described simply by an effective temperature. 
M. Florencia Carusela and Joachim Ankerhold
cond-mat.mes-hall