Rabi oscillations at the exceptional point in anti-parity-time symmetric diffusive systems

The motivation for this theoretical paper comes from recent experiments of a heat transfer system of two thermally coupled rings rotating in opposite directions with equal angular velocities that present anti-parity-time (APT) symmetry. The theoretical model predicted a rest-to-motion temperature distribution phase transition during the symmetry breaking for a particular rotation speed. In this work we show that the system exhibits a parity-time $mathcal{PT}$ phase transition at the exceptional point in which eigenvalues and eigenvectors of the corresponding non-Hermitian Hamiltonian coalesce. We analytically solve the heat diffusive system at the exceptional point and show that one can pass through the phase transition that separates the unbroken and broken phases by changing the radii of the rings. In the case of unbroken mathcal{PT} symmetry the temperature profiles exhibit damped Rabi oscillations at the exceptional point. Our results unveils the behavior of the system at the exceptional point in heat diffusive systems.