Exponential sensitivity to dephasing of electrical conduction through a   quantum dot
  According to random-matrix theory, interference effects in the conductance of a ballistic chaotic quantum dot should vanish $\propto(\tau_{\phi}/\tau_{D})^{p}$ when the dephasing time $\tau_{\phi}$ becomes small compared to the mean dwell time $\tau_{D}$. Aleiner and Larkin have predicted that the power law crosses over to an exponential suppression $\propto\exp(-\tau_{E}/\tau_{\phi})$ when $\tau_{\phi}$ drops below the Ehrenfest time $\tau_{E}$. We report the first observation of this crossover in a computer simulation of universal conductance fluctuations. Their theory also predicts an exponential suppression $\propto\exp(-\tau_{E}/\tau_{D})$ in the absence of dephasing -- which is not observed. We show that the effective random-matrix theory proposed previously for quantum dots without dephasing explains both observations. 
J. Tworzydlo, A. Tajic, H. Schomerus, P. W. Brouwer, and C.W.J.   Beenakker