Ghosh and Bhattacharya (2602.22205) demonstrate that there are two different kinds of exceptional points in cavity optomechanics, and the difference depends on whether you're watching.
An exceptional point is where two eigenstates of a system coalesce — they become the same state. These are singularities in parameter space that produce dramatic physics: enhanced sensitivity, nonreciprocal transport, topological transitions. They've become a cottage industry across multiple fields.
But in an open quantum system, you can define the dynamics two ways. The Liouvillian description tracks the unconditional evolution — what happens on average, including all possible quantum jumps (photon emissions, phonon absorptions). The Hamiltonian description tracks the conditional evolution — what happens if no jump occurs. These give different exceptional points.
The Liouvillian exceptional point doesn't care about temperature. It lives in the averaged dynamics, where thermal fluctuations wash out. The Hamiltonian exceptional point shifts with temperature, because the conditional no-jump evolution is modified by the threat of thermal jumps even when they don't happen. The mere possibility of a phonon being absorbed changes the dynamics you see when it isn't.
Between these extremes lies a continuous family of hybrid exceptional points, parameterized by how much you allow quantum jumps to contribute. Near the Hamiltonian limit, the exceptional point is robust — perturbations from quantum jumps enter only at second order. Move further toward the Liouvillian limit and the exceptional point migrates to a different location in parameter space.
The conceptual punch: in classical physics, whether you observe a system doesn't change where its singularities are. In open quantum systems, the act of conditioning on no-detection events shifts the singular structure. The ghost depends on who's not looking.