Spin precession caused by spin-spin interaction between bounded electrons in quantum dots

In this paper, we study the spin-spin interaction between two electrons bounded in a quantum dot. The result shows that spin-spin interaction will cause a pair of spins precessing synchronously. If the two spins are parallel at initial time, the total spin oscillates as a cosine function. If the two spins are antiparallel at initial time, the total spin keeps zero. The precessing period is proportional to the cube of quantum dot radius. For a 2D round quantum dot with radius $R=50{\text{nm}}$, the precessing period equals nearly $12\mu {\text{s}}$.