  Logarithmic or Sinai type subdiffusion is usually associated with random
force disorder and non-stationary potential fluctuations whose root mean
squared amplitude grows with distance. We show here that extremely persistent,
macroscopic ultraslow logarithmic diffusion also universally emerges at
sufficiently low temperatures in stationary Gaussian random potentials with
spatially decaying correlations, known to exist in a broad range of physical
systems. Combining results from extensive simulations with a scaling approach
we elucidate the physical mechanism of this unusual subdiffusion. In
particular, we explain why with growing temperature and/or time a first
crossover occurs to standard, power-law subdiffusion, with a time-dependent
power law exponent, and then a second crossover occurs to normal diffusion with
a disorder-renormalized diffusion coefficient. Interestingly, the initial,
nominally ultraslow diffusion turns out to be much faster than the universal de
Gennes-Baessler-Zwanzig limit of the renormalized normal diffusion, which
physically cannot be attained at sufficiently low temperatures and/or for
strong disorder. The ultraslow diffusion is also non-ergodic and displays a
local bias phenomenon. Our simple scaling theory not only explains our
numerical findings, but qualitatively has also a predictive character.
