Fig. \[fig:transmission\_bounds\] for the cases of $\ell=0$ and $1$, respectively. There the transmission coefficients (ie. $T^{(\ell)}_{\infty,n}$) for large values of the scattering length are compared to the quasi 1D unitarity bound, i.e. the bound to the transmission coefficient at a CIR ie. $T^{(\ell)}_{\rm{CIR},n}$.

To understand the behavior of the transmission coefficient at a CIR, recall that the denominator of Eq. represents $\det(\openone-i{\mathbf{K}_{cc}^{1D}})$, which implies, that if this expression vanishes for a particular value of $\Delta_\ell$, or the corresponding scattering length, respectively, a CIR occurs. We hence have a sufficient criterion for the occurrence of a CIR given by the condition $\alpha_{\ell}\rightarrow\infty$, with $\alpha_{\ell}$ from Eq. . A transmission value of $T=0$ can only be achieved in the [$s$-SPWA]{} when there is a single open channel, since then ${\operatorname{Tr}[{\mathbf{F}_{\ell\ell}^{\mathbf{o}}}]}={\mathbf{F}_{\ell\ell}^{\mathbf{o}}}$ holds. From a physical point of view this behavior is expected, since a transmission blockade in a specific channel will not prevent the scattering into other channels, which for example can be seen in Fig. \[fig:transmission\_transistion\_12\_bosons\], where the transmission coefficients ${T_{0}^{(0)}}$ and ${T_{1}^{(0)}}$ are shown, respectively. Both curves exhibit minima at the CIR. Also in Fig. \[fig:transmission\_transistion\_12\_bosons\] we plot the transition coefficient $W_{01}^{(0)}$ (dotted lines) which is enhanced at a CIR clearly 