  We propose a novel one-dimensional simple model without disorder exhibiting
slow dynamics and aging at the zero temperature limit. This slow dynamics is
due to entropic barriers. We exactly solve the statics of the model. We derive
an evolution equation for the slow modes of the dynamics which are responsible
for the aging. This equation is equivalent to a random walker on the energetic
landscape. This latter elementary model can be solved analytically up to some
basic approximations and is eventually shown to present aging by itself, as
well as a slow logarithmic relaxation of the energy: e(t) ~ 1/ln(t) at large t.
