Time-dependent Aharonov-Casher effect on noncommutative space

In this paper, we study the time-dependent Aharonov-Casher effect and its corrections due to spatial noncommutativity. Given that the charge of the infinite line in the Aharonov-Casher effect can adiabatically vary with time, we show that the original Aharonov-Casher phase receives an adiabatic correction, which is characterized by the time-dependent charge density. Based on Seiberg-Witten map, we show that noncommutative corrections to the time-dependent Aharonov-Casher phase contains not only an adiabatic term but also a constant contribution depending on the frequency of the varying electric field.