Inverse temperature dependent energy diffusion in positive and negative temperature regimes for the 1d coupled rotator lattice with bounded kinetic energy

The negative temperature with Boltzmann description can be realized in Hamiltonian with bounded energy terms such as the 1d coupled rotator lattice with bounded kinetic energy. Normal heat conduction behavior has also been found for this 1d nonlinear lattice model. In this paper, we will systematically investigate the energy diffusion behavior for such 1d nonlinear lattice in both the positive and negative temperature regimes via equilibrium diffusion method. Normal energy diffusion is confirmed with Gaussian fitting and inverse temperature dependent energy diffusion constants are obtained over the whole temperature range.