Emergence of quasiperiodic behaviour in transport and hybridisation properties of clean lattice systems

Quasiperiodic behaviour is mostly known to occur in systems with enforced quasiperiodicity, in either the lattice structure or the potential, as well as in periodically driven systems. Here, we present instead a rarer setting where quasiperiodic behaviour emerges in clean, non-driven lattice systems. We illustrate this through two examples of experimental relevance, namely an infinite tight-binding chain with a gated segment, and a hopping particle coupled to static Ising degrees of freedom. We show how the quasiperiodic behaviour manifests in the number of states that are localised by the geometry of the system, with corresponding effects on transport and hybridisation properties.