Inhibition of non-Hermitian topological phase transitions in sliding photonic quasicrystals

Non-Hermitian (NH) quasicrystals have been a topic of increasing interest in current research, particularly in the context of NH topological physics and materials science. Recently, it has been suggested and experimentally demonstrated using synthetic photonic lattices that a class of NH quasicrystals can feature topological spectral phase transitions. Here we consider a NH quasicrystal with a uniformly-drifting (sliding) incommensurate potential and show that, owing to violation of Galilean invariance, the topological phase transition is washed out and the quasicrystal is always in the delocalized phase with an entirely real-energy spectrum. The results are illustrated by considering quantum walks in synthetic photonic lattices.