Logarithmically slow heat propagation in a clean Josephson-junction chain

Abstract

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.

Figures (2)

• Figure 1: Circuit scheme of the Josephson junction chain. Notice the coupling to the resistance through the leftmost site. Each node (red circles) corresponds to a superconducting island and is labeled with an index $j$ going from 1 to $L$. Each capacitor has a capacitance $C$ and a charging energy $E_C = (2e)^2/C$, and each Josephson junction a Josephson energy $E_J$.
• Figure 2: (Panel a) Thermalization length $h(t)$ [see Eq. \ref{['leng:eqn']}] versus time $t$, with the horizontal axis plotted in a logarithmic scale, for different values of the reduced temperature $\tau$. We see a quite clear logarithmic increase after a prethermal transient where $h(t)$ is vanishing. (Panel b) Energy $\braket{\mathcal{H}}_t$ versus time $t$ with the horizontal axis in a logarithmic scale. Notice the logarithmic increase in time after an initial prethermal plateau, quite evident for the larger values of the reduced temperature $\tau$. Numerical parameters: $N_{\rm r} = 990,\,\Delta t = 10^{-4},\,E_J = 10^{-2},\,RC = 1,\,E_C = 1,\,L=20$.