We consider a ladder system where one leg, referred to as the “bath,” is governed by an Aubry-André (AA)-type Hamiltonian, while the other leg, termed the “subsystem,” follows a standard tight-binding Hamiltonian. We investigate the localization properties in the subsystem induced by its coupling to the bath. For the coupling strength larger than a critical value ($t^{\prime }>t_c^{\prime }$), the analysis of the static properties shows that there are three distinct phases as the AA potential strength $V$ is varied: a fully delocalized phase at low $V$, a localized phase at intermediate $V$, and a weakly delocalized (fractal) phase at large $V$. The fractal phase also appears in a narrow region along the boundary between the delocalized and localized phases. An analysis of the projected wave-packet dynamics in the subsystem shows that the delocalized phase exhibits a ballistic behavior, whereas the weakly delocalized phase is subdiffusive. Interestingly, the narrow fractal phase shows a super- to subdiffusive behavior as we go from the delocalized to localized phase. When $t^{\prime }<t_c^{\prime }$, the intermediate localized phase disappears and we find a delocalized (ballistic) phase at low $V$ and a weakly delocalized (subdiffusive) phase at large $V$. Between those two phases, there is also an anomalous crossover regime where the system can be super- or subdiffusive. Beyond the ballistic phase observed at low $V$, we also identify a superdiffusive regime emerging in the limit $t^{\prime }/V\ll 1$, which continuously approaches the ballistic behavior as $t^{\prime }\to 0$. Finally, in some limiting scenario, we also establish a mapping between our ladder system and a well-studied one-dimensional generalized Aubry-André (GAA) model.

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• Localization
• Quantum transport
• 1-dimensional systems
• Quasicrystals
• Numerical techniques