Electric and magnetic field induced geometric phases for the 2D harmonic oscillator in noncommutative phase space

In this work, we point out the phenomenon whereby the noncommutative corrections to the geometric phases induced by an electric field and a magnetic field have different orders in terms of the noncommutative parameters. The first order correction is zero for the electric field induced geometric phase and it is nonzero for the magnetic field induced geometric phase. In our calculation, the system is in coherent states when the electric field is applied, so the corresponding geometric phase calculated is that of the coherent states. Considering that the noncommutative parameters are very small, it is better to use the magnetic field rather than the electric field for detecting the noncommutativity of spaces.