  Quasi-periodic lattice systems offer diverse transport properties. In this
work, we investigate the environment induced effects on transport properties
for quasi-periodic systems, namely the one-dimensional Aubry-Andr\'e-Harper
(AAH) lattice chain and its generalized version (GAAH) by considering the
B\"uttiker probe approach. We first consider voltage probe situation and study
the electrical conductance properties in the linear response regime. At zero
temperature, we observe enhancement in conductance at all the no-transport
regimes, located both inside and outside of the band of the original system,
for small probe coupling strength $\gamma$ with a power-law scaling $\gamma^4$.
Whereas, for large probe coupling strengths, the conductance at all Fermi
energies is the same and decays as a power-law with scaling $1/\gamma^4$. This
particular scaling survives even in the finite-temperature limit.
Interestingly, this scaling result is different from the one recently predicted
following the local Lindblad master equation approach. The transport eventually
becomes diffusive for all energy ranges and in all regimes of the original
model for a sufficiently strong coupling with the probes. We further extend our
study and consider voltage-temperature probes to analyze the thermoelectric
performance of the chain in terms of the figure of merit. We also demonstrate
the validity of two recently obtained bounds on thermoelectric efficiency that
are tighter than the seminal Carnot bound and express the same in terms of the
Onsager's transport coefficients.
