Thermodynamic modes of a quasiperiodic mobility-edge system in a quantum Otto cycle

We investigate thermodynamic operation of a quasiperiodic lattice with an exact mobility edge, described by the Biddle--Das Sarma model. We use this model as the working medium of a quantum Otto cycle and map its operating mode as a function of the hopping-range parameter $p$, the initial and final potential strengths $V_i$ and $V_f$, and two idealized protocols for the isolated strokes. In a near-adiabatic (state-frozen) protocol, where the density matrix is approximately unchanged during the isolated strokes, the cycle supports only two modes: a \emph{heater} and an \emph{accelerator}. In an adiabatic protocol, where level populations are preserved while the spectrum is deformed, two additional modes appear: a \emph{heat engine} and a \emph{refrigerator}. Our results show that mobility-edge systems can realize multiple thermodynamic functions within a single platform and provide guidance for switching between modes by tuning $p$, $V_i$, and $V_f$.