  We develop a theory of spin noise in semiconductor nanowires considered as
prospective elements for spintronics. In these structures spin-orbit coupling
can be realized as a random function of coordinate correlated on the spatial
scale of the order of 10 nm. By analyzing different regimes of electron
transport and spin dynamics, we demonstrate that the spin relaxation can be
very slow and the resulting noise power spectrum increases algebraically as
frequency goes to zero. This effect makes spin effects in nanowires best
suitable for studies by rapidly developing spin-noise spectroscopy.
