Quantum metric and wavepackets at exceptional points in non-Hermitian systems

The usual concepts of topological physics, such as the Berry curvature, cannot be applied directly to non-Hermitian systems. We show that another object, the quantum metric, which often plays a secondary role in Hermitian systems, becomes a crucial quantity near exceptional points in non-Hermitian systems, where it diverges in a way that fully controls the description of wavepacket trajectories. The quantum metric behaviour is responsible for a constant acceleration with a fixed direction, and for a non-vanishing constant velocity with a controllable direction. Both contributions are independent of the wavepacket size.