  Brownian particles suspended in disordered crowded environments often exhibit
non-Gaussian normal diffusion (NGND), whereby their displacements grow with
mean square proportional to the observation time and non-Gaussian statistics.
Their distributions appear to decay almost exponentially according to
"universal" laws largely insensitive to the observation time. This effect is
generically attributed to slow environmental fluctuations, which perturb the
local configuration of the suspension medium. To investigate the microscopic
mechanisms responsible for the NGND phenomenon, we study Brownian diffusion in
low dimensional systems, like the free diffusion of ellipsoidal and active
particles, the diffusion of colloidal particles in fluctuating corrugated
channels and Brownian motion in arrays of planar convective rolls. NGND appears
to be a transient effect related to the time modulation of the instantaneous
particle's diffusivity, which can occur even under equilibrium conditions.
Consequently, we propose to generalize the definition of NGND to include
transient displacement distributions which vary continuously with the
observation time. To this purpose, we provide a heuristic one-parameter
function, which fits all time-dependent transient displacement distributions
corresponding to the same diffusion constant. Moreover, we reveal the existence
of low dimensional systems where the NGND distributions are not leptokurtic
(fat exponential tails), as often reported in the literature, but platykurtic
(thin sub-Gaussian tails), i.e., with negative excess kurtosis. The actual
nature of the NGND transients is related to the specific microscopic dynamics
of the diffusing particle.
