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Logarithmic or Sinai type subdiffusion is usually associated with randomforce disorder and non-stationary potential fluctuations whose root meansquared amplitude grows with distance. We show here that extremely persistent,macroscopic ultraslow logarithmic diffusion also universally emerges atsufficiently low temperatures in stationary Gaussian random potentials withspatially decaying correlations, known to exist in a broad range of physicalsystems. Combining results from extensive simulations with a scaling approachwe elucidate the physical mechanism of this unusual subdiffusion. Inparticular, we explain why with growing temperature and/or time a firstcrossover occurs to standard, power-law subdiffusion, with a time-dependentpower law exponent, and then a second crossover occurs to normal diffusion witha disorder-renormalized diffusion coefficient. Interestingly, the initial,nominally ultraslow diffusion turns out to be much faster than the universal deGennes-Baessler-Zwanzig limit of the renormalized normal diffusion, whichphysically cannot be attained at sufficiently low temperatures and/or forstrong disorder. The ultraslow diffusion is also non-ergodic and displays alocal bias phenomenon. Our simple scaling theory not only explains ournumerical findings, but qualitatively has also a predictive character.

Persistent Sinai type diffusion in Gaussian random potentials with decaying spatial correlations