Maxwell Duality, Lorentz Invariance, and Topological Phase

Dowling, Jonathan P.; Williams, Colin P.; Franson, J. D.

doi:10.1103/physrevlett.83.2486

Cited by 109 publications

(101 citation statements)

References 28 publications

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“…Although the effect for ±q charged particles is viable [21], the technology and interferometry for the test of this effect needs improvements. It is worth recalling that not long ago the technology and interferometry for beams of particles with opposite magnetic ±m or electric ±d dipole moments was likewise unavailable, but is today a reality [24] [28]. Discussions on this subject may act as a stimulating catalyst for further studies and technological advances that will lead to the experimental test of this quantum effect.…”

Section: Phase Of Effect S In Nc Quantum Mechanics and Limit Over θmentioning

confidence: 99%

Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

Rodriguez

2018

Phys. Rev. A

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Quantum mechanics in noncommutative space modifies the standard result of the Aharonov-Bohm effect for electrons and other recent quantum effects. Here we obtain the phase in noncommutative space for the Spavieri effect, a generalization of Aharonov-bohm effect which involving a coherent superposition of particles with opposite charges moving along single open interferometric path. By means of the experimental considerations a limit √ θ ≃ (0, 13T eV) −1 is achieved, improving by 10 orders of magnitude the derived by Chaichian et. al. for the Aharonov-Bohm effect. It is also shown that the noncommutative phases of the Aharonov-Casher and He-McKellar-Willkens effects are nullified in the current experimental tests.

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Section: Phase Of Effect S In Nc Quantum Mechanics and Limit Over θmentioning

confidence: 99%

Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

Rodriguez

2018

Phys. Rev. A

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“…The HMW effect was firstly discussed in 1993 by He and Meckellar [7] and a year later, independently by Wilkens [8]. The HMW effect corresponds to a topological phase related to a neutral spin-1/2 particle with non-zero electric dipole moving in the magnetic field, and in 1998, Dowling, Willianms and Franson point out that the HMW effect can be partially tested using metastable hydrogen atoms [9]. Just as the AB AC effect, the HMW effect has the same importance in the literature, and the study of the correction of the space (and momenta) non-commutativity to the HMW effect will be meaningful.…”

Section: Introductionmentioning

confidence: 99%

“…we study the problem on NC phase space, the Dirac equation for the HMW model is the same as the case on NC space, but the star product and the shifts are defined in Eqs. (7) and (9). After a similar procedure as in NC space, we got the Dirac equation on NC phase space as:…”

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confidence: 99%

The HMW effect in noncommutative quantum mechanics

Wang¹,

Li²

2007

J. Phys. A: Math. Theor.

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“…Its Maxwell dual phase is the He-Mckellar-Wilkens (HMW) phase which implies that a neutral particle with a non-zero electric dipole moment moving around a line of magnetic monopoles would accumulate a quantum phase. [6] Wei, Han and Wei proposed a practical experimental configuration to test this effect [7], and Dowling et al proposed two other experimental schemes for it [8]. Recently, another non-dispersive quantum geometrical phase was proposed by Anandan.…”

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confidence: 99%

Two-dimensional noncommutative atom gas with the Anandan interaction

Xiao-Min

2011

Phys. Rev. A

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Landau like quantization of the Anandan system in a special electromagnetic field is studied. Unlike the cases of the AC system and the HMW system, the torques of the system on the magnetic dipole and the electric dipole don't vanish. By constructing Heisenberg algebra, the Landau analog levels and eigenstates on commutative space, NC space and NC phase space are obtained respectively. By using the coherent state method, some statistical properties of such free atom gas are studied and the expressions of some thermodynamic quantities related to revolution direction are obtained. Two particular cases of temperature are discussed and the more simple expressions of the free energy on the three spaces are obtained. We give the relation between the value of σ and revolution direction clearly, and find Landau like levels of the Anandan system are invariant and the levels between the AC system and the HMW system are interchanged each other under Maxwell dual transformations on the three spaces. The two sets of eigenstates labelled by σ can be related by a supersymmetry transformation on commutative space, but the phenomenon don't occur on NC situation. We emphasize that some results relevant to Anandan interaction are suitable for the cases of AC interaction and HMW interaction under special conditions.

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Maxwell Duality, Lorentz Invariance, and Topological Phase

Cited by 109 publications

References 28 publications

Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

The HMW effect in noncommutative quantum mechanics

Two-dimensional noncommutative atom gas with the Anandan interaction

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