Logarithmically slow heat propagation in a clean Josephson-junction chain

We consider a clean Josephson-junction chain coupled by one of its extremities to a thermal bath through a resistance. Considering the Langevin dynamics in the classical regime, in the case of Josephson energy much smaller than charging energy, we find that heat propagates logarithmically slowly through the system, rather than diffusively, as highlighted by the logarithmic increase in time of a thermalization length we define and by the logarithmically slow increase in time of the energy. This behavior -- typical of quantum Anderson or many-body localized systems -- is observed here also in a clean classical glassy Hamiltonian system. We argue that this phenomenon might imply strong robustness to the effect of ergodic inclusions for the nonergodic behavior in the charge-quantized regime.