Controlled wave acceleration in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric and inhomogeneous non-Hermitian lattices

We report the propagation of fast and stable wave packets in classical non-Hermitian lattices, where the group velocity is controlled by the non-Hermiticity parameters, and can exceed that of the Hermitian counterpart. Specifically, we design a $\mathcal{PT}$-symmetric system that supports a constant group velocity increase, and which evolves into a nonconstant increase, i.e., an acceleration, when we induce spatial inhomogeneity. A dedicated relation between the control parameters keeps the lattice system dynamically stable for the achieved velocities. As a result, wave packets are propagating along the lattice with a nongrowing amplitude. We demonstrate the system experimentally in a topoelectrical metamaterial, where the non-Hermiticity is generated by embedded operational amplifiers in a feedback setup. Our design paves the way to new forms of fast and stable signal transmission, which can be directly controlled on demand.