Although we are gratified that the mechanism proposed by Avenel et al. for the π-state expands on our previous conjecture1 that internally trapped circulating currents could be involved in its existence, we do not believe that it is the only possible explanation. This is because agreement between a given data set and a numerical simulation, using a model with several adjustable parameters, represents a check that the model is consistent with the data, but does not qualify as a proof of the model4. Therefore, we cannot say to what extent their model represents physical reality better than other theories of the π-state that have been recently proposed5.

However, several aspects of their simulation disagree with our experimental observations. In particular, the model presented by Avenel et al. does not seem to conserve energy in the oscillator, contrary to our experimental results. Their model predicts that the I(φ) relation should extend beyond φ = π before the onset of the π-state. In contrast, the collapse into the π-state occurs at φ<π. finally, as shown in their Fig. 1c and supported by our own simulations, their model leads to metastable states at positions other than π, a feature also in contradiction to the data.

Figure 1: Numerical simulations.
figure 1

a, Current-phase relationship for α = 2. Dotted line, artefact of the measurements in an array of holes discussed in the text. b, Time evolution of the membrane amplitude X in response to an external drive Vex. c, Corresponding trajectory in the d(φ*)/dt versus φ* plane.

We hope that Avenel et al. will continue to refine their simulations to make predictions that could lead to a conclusive test of their underlying model.

See also Avenel et al.