  We present a detailed analytical and numerical analysis of the nuclear spin
dynamics in parabolic quantum wells. The shallow potential of parabolic quantum
wells permits substantial modification of the electronic wave function in small
electric fields. The nuclear spin relaxation via the hyperfine interaction
depends on the electronic local density of states, therefore the local nuclear
relaxation time depends sensitively on the electric field. For an inhomogeneous
nuclear magnetization, such as generated by dynamic nuclear polarization, the
total nuclear magnetization dynamics can similarly be altered. We examine this
effect quantitatively and the effect of temperature, field, well thickness, and
nuclear spin diffusion.
