  We investigate the observables of the one-dimensional model for anomalous
transport in semiconductor devices where diffusion arises from scattering at
dislocations at fixed random positions, known as L\'evy-Lorentz gas. Due to
complex stochasticity in the system, direct investigations of such non-trivial
dynamics are not possible; therefore, to gain insight into the microscopic
properties, we use deterministic dynamics known as the Slicer Map and
Fly-and-Die dynamics. We analytically derive the generalized position
auto-correlation function of these dynamics and study the special case, the
3-point position correlation function. For this, we derive single
parameter-dependent scaling and compare it with the numerically estimated
3-point position auto-correlation of the L\'evy-Lorentz gas, for which the
analytical expression is still an open question. Here we obtained a remarkable
agreement between them, irrespective of any functional relationship with time.
Moreover, we demonstrate that the position moments and the position
auto-correlations of these systems scale in the same fashion, provided the
times are large enough and far enough apart. Other observables, such as
velocity moments and correlations, are reported to distinguish the systems.
