Electric and magnetic eld induced geometric phases for the 2D harmonicoscillator in noncommutative phase space

Abstract

In this work, we point out the phenomenon whereby the noncommutative corrections to the geometric phasesinduced by an electric eld and a magnetic eld have di erent orders in terms of the noncommutative parameters. The rst order correction is zero for the electric eld induced geometric phase and it is nonzero for the magnetic eld inducedgeometric phase. In our calculation, the system is in coherent states when the electric eld is applied, so the correspondinggeometric phase calculated is that of the coherent states. Considering that the noncommutative parameters are verysmall, it is better to use the magnetic eld rather than the electric eld for detecting the noncommutativity of spaces.