  Rugged energy landscapes find wide applications in diverse fields ranging
from astrophysics to protein folding. We study the dependence of diffusion
coefficient $(D)$ of a Brownian particle on the distribution width
$(\varepsilon)$ of randomness in a Gaussian random landscape by simulations and
theoretical analysis. We first show that the elegant expression of Zwanzig
[PNAS, 85, 2029 (1988)] for $D(\varepsilon)$ can be reproduced exactly by using
the Rosenfeld diffusion-entropy scaling relation. Our simulations show that
Zwanzig's expression overestimates $D$ in an uncorrelated Gaussian random
lattice - differing by almost an order of magnitude at moderately high
ruggedness. The disparity originates from the presence of "three-site traps"
(TST) on the landscape -- which are formed by the presence of deep minima
flanked by high barriers on either side. Using mean first passage time
formalism, we derive a general expression for the effective diffusion
coefficient in the presence of TST, that quantitatively reproduces the
simulation results and which reduces to Zwanzig's form only in the limit of
infinite spatial correlation. We construct a continuous Gaussian field with
inherent correlation to establish the effect of spatial correlation on random
walk. The presence of TSTs at large ruggedness $(\varepsilon \gg k_{B}T)$ give
rise to an apparent breakdown of ergodicity of the type often encountered in
glassy liquids.
