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We have studied analytically the persistent current and the magnetization of two electrons trapped by a circular parabolic GaAs quantum dot using the canonical ensemble approach. We have investigated their behavior as a function of the dot size and magnetic field in the presence and the absence of the harmonic e-e interaction at high and low temperatures. Our investigations reveal that the diamagnetic state is the preferred state for the persistent current and magnetization. As a function of the dot size, initially the current is entirely independent of the interaction and it remains constant up to a certain value of the dot size beyond which it increases significantly and the effect of the harmonic interaction becomes tangible in the low-temperature limit. However as a function of the magnetic field at high temperatures, the current takes a diminishing linear form and this decrease is noticeable for narrower dots, but at extremely low temperatures, the current becomes insensitive to the interaction for a dot with small size. As a function of temperature, the current increases sharply with temperature and then tends to saturate as the temperature becomes slightly larger. This study demonstrates a comparison between the current and the magnetization. Our results show that, as a function of temperature, they qualitatively exhibit the same behavior and they are proportional to each other in the presence of weak magnetic field, while as a function of the magnetic field, they display non-similar behavior at low temperatures.

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