Time-dependent Aharonov–Casher effect on noncommutative space

Abstract

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.