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Transport characteristics in Hermitian and non-Hermitian Fibonacci rings: A comparative study

We present an extensive theoretical analysis of transport and circular currents and the associated induced magnetic fields in Fibonacci rings, explored in both Hermitian and non-Hermitian descriptions, with particular attention to configurations preserving or breaking PT symmetry. By engineering physically balanced gain and loss following a Fibonacci sequence, we realize two distinct geometrical configurations in which the ring either preserve or explicitly break PT symmetry, and further explore complementary realizations obtained by reversing the signs of the on site potentials. Using the non equilibrium Green's function (NEGF) formalism, we analyze transmission properties and bond current densities to quantify both transport and circulating currents. A comparison with the Hermitian limit establishes a clear baseline, where the ring supports only weak responses upon introducing disorder. In sharp contrast, non-Hermiticity leads to a pronounced amplification of transport and circular currents, and hence of the induced magnetic field. We further demonstrate that non-Hermitian transport is highly sensitive to gain and loss sign reversal and, in the non-PT-symmetric case, exhibits an unconventional dependence on system size governed by the parity of the Fibonacci sequence and hopping correlations. Remarkably, the current does not decay monotonically with increasing system size, revealing a distinct scaling behavior absent in conventional Hermitian systems. Our results highlight non-Hermitian quasiperiodic rings as versatile platforms for engineering and amplifying current driven magnetic responses through symmetry, topology, and gain-loss design.