We consider a model inspired by a metal break-junction hypothetically caught at its breaking point, where the non-adiabatic center-of-mass motion of the bridging atom can be treated as a two-level system. By means of Numerical Renormalization Group (NRG) we calculate the influence of the two level system on the ballistic conductance across the bridge atom. The results are shown to be fully consistent with a conformal field theory treatment. We find that the conductance, calculated by coupling Fermi liquid theory to our NRG is always finite and fractional at zero temperature, but drops quite fast as the temperature increases.
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