We investigate quantum dynamics of the superconducting phase in intrinsic Josephson junctions of layered high-Tc superconductors motivated by a recent experimental observation for the switching rate enhancement in the low temperature quantum regime. We pay attention to only the capacitive coupling between neighboring junctions and perform large-scale simulations for the Schrödinger equation derived from the Hamiltonian considering the capacitive coupling alone. The simulation focuses on an issue whether the switching of a junction induces those of the other junctions or not. The results reveal that the superconducting phase dynamics show synchronous behavior with increasing the quantum character, e.g., decreasing the junction plane area and effectively the temperature. This is qualitatively consistent with the experimental result.
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