Figure 7

Validity of the quartic approximation. Ratio $N_{\mathrm{crit}}/N_{\max }$ according to Eq. (40) (black), in the lumped element limit (dashed blue) and in the limit of small participation ratio $L_J\ll ld$ (dotted red) for the parameters $\{{\tilde{\omega }}_0/2\pi ,Q\}=\{7\text{GHz},1,000\}$.