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We present formulas for the nuclear and electronic spin relaxation times dueto the hyperfine interaction for nanostructed systems and show that the timesdepend on the square of the local density of electronic states at the nuclearposition. A drastic sensitivity (orders of magnitude) of the electronic andnuclear spin coherence times to small electric fields is predicted for bothuniformly distributed nuclear spins and for $\d$-doped layers of specificnuclei. This sensitivity is robust to nuclear spin diffusion.Comment: 4 pages, 3 figures, revtex

Electric Field Tunability of Nuclear and Electronic Spin Dynamics due to the Hyperfine Interaction in Semiconductor Nanostructures