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.
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