The kicked quantum rotor (a particle freely moving on a circle
subject to periodic delta-kicks) has been studied for decades
and is one of the most popular models of quantum chaos. The
dynamics of the classical version of the model corresponds
to the diffusive random walk in the angular momentum space
and constant energy absorption. The quantum dynamics
exhibits a phenomenon of the dynamic localization
(suppression of the classical diffusion by destructive quantum
interference), as was discovered numerically by Casati et al. in
1979, and was believed to be proven analytically in 1996 by
Altland and Zirnbauer. I would like to discuss a very recent
preprint by Tian, Kamenev and Larkin (cond-mat/0403482) which
reexamines the question of quantum corrections to the diffusion,
and brings to light certain effects apparently missed by the
approach of Altland and Zirnbauer