We study a system in which electrons in a two-dimensional electron gas are
confined by a nonhomogeneous nuclear spin polarization. The system consists of
a heterostructure that has non-zero nuclei spins. We show that in this system
electrons can be confined into a dot region through a local nuclear spin
polarization. The nuclear-spin-polarization-induced quantum dot has interesting
properties indicating that electron energy levels are time-dependent because of
the nuclear spin relaxation and diffusion processes. Electron confining
potential is a solution of diffusion equation with relaxation. Experimental
investigations of the time-dependence of electron energy levels will result in
more information about nuclear spin interactions in solids
