  We reveal the mechanism of subdiffusion which emerges in a straightforward,
one dimensional classical nonequilibrium dynamics of a Brownian ratchet driven
by both a time-periodic force and Gaussian white noise. In a tailored parameter
set for which the deterministic counterpart is in a non-chaotic regime,
subdiffusion is a long-living transient whose lifetime can be many, many orders
of magnitude larger than characteristic time scales of the setup thus being
amenable to experimental observations. As a reason for this subdiffusive
behaviour in the coordinate space we identify thermal noise induced dynamical
localization in the velocity (momentum) space. This novel idea is distinct from
existing knowledge and has never been reported for any classical or quantum
systems. It suggests reconsideration of generally accepted opinion that
subdiffusion is due to road distributions or strong correlations which reflect
disorder, trapping, viscoelasticity of the medium or geometrical constraints.
