Thermalization without dissipation in superconducting circuits

In a closed system composed of coupled, weakly nonlinear resonators, the non-linearity leads to thermalization among the resonant modes by enabling energy transfer among the modes in a chaotic fashion. Such thermalization without dissipation is identified upon the system reaching equilibrium by the classical Rayleigh-Jeans distribution that relates the mode occupancies of the resonances to the eigen-energies. We demonstrate this effect in planar superconducting devices, presenting numerical simulations and experimental results in capacitively coupled resonators that include Josephson junctions as the non-linear inductor. To emulate closed system dynamics, the rate of dissipation is made much longer than the thermalization rate by increasing the quality factors of the resonators. This study can be further extended to investigate quantum thermodynamics by increasing the non-linearity and lowering the energy scale of the system.