Non-commutative quantum mechanics and the Aharonov-Casher effect

Abstract

In this work a new method is developed to investigate the Aharonov-Casher effect in a noncommutative space. It is shown that the holonomy receives non-trivial kinematical corrections.

Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

“…[8] for the AB effect where the kinetic term is five orders greater than the geometric term. Consequently, for the estimation of the limit on θ we consider only the first term in brackets of expression (12)…”

Aharonov-Bohm Phase for an Electric Dipole on a Noncommutative Space

“…The authors of Zhang [11] have suggested the possibility of testing spatial noncommutativity via cold Rydberg atoms. In Chaichian et al [12], Chaichian et al [13], Falomir et al [14], Li and Dulat [15], Mirza and Zarei [16], Li and Wang [17], Mirza et al [18], Singlton and Vagenas [19], Dulat and Ma [20] and Singleton and Ulbricht [21], the AharonovBohm type phase is studied on a NCS and a NCPS. A lower bound is shown to be 1/ √ θ ≥ 10 −6 GeV for the space noncommutativity parameter in Chaichian et al [12].…”

“…A lower bound is shown to be 1/ √ θ ≥ 10 −6 GeV for the space noncommutativity parameter in Chaichian et al [12]. In Mirza and Zarei [16], Li and Wang [17] and Mirza et al [18,22], the Aharonov-Casher phase on a NCS and a NCPS has been studied for a spin-1/2 and a spin-1 particle. And in Mirza and Zarei [16] the limit for the space noncommutativity parameter is 1/ √ θ ≥ 10 −7 GeV.…”

“…In Mirza and Zarei [16], Li and Wang [17] and Mirza et al [18,22], the Aharonov-Casher phase on a NCS and a NCPS has been studied for a spin-1/2 and a spin-1 particle. And in Mirza and Zarei [16] the limit for the space noncommutativity parameter is 1/ √ θ ≥ 10 −7 GeV. The authors of Harms and Micu [23], Dayi and Jellal [24] and Chakraborty et al [25][26][27][28][29][30] have studied the noncommutative quantum Hall effect, and in Harms and Micu [23] a limit of 1/ √ θ ≥ 10GeV is given.…”

Функции Вигнера Для Задачи Ландау В Некоммутативной Квантовой Механике

“…Кро-ме того, имеется много работ, посвященных теоретико-полевым исследованиям раз-личных аспектов квантовой механики в НКП и НКФП с обычными (коммутатив-ными) временными координатами [1]- [11]. Например, фаза Ааронова-Бома в НКП и НКФП исследовалась в работах [1]- [3], а фаза Ааронова-Кашера для частиц со спином 1/2 и спином 1 в НКП и НКФП -в работах [4], [5]. В работах [6], [7] рас-сматривались задача Ландау и эффект Хе-Мекеллара-Вилкенса как в НКП, так и в НКФП.…”