A New Version of the Aharonov–Bohm Effect

Oliveira, César R. de; Romano, Renan G.

doi:10.1007/s10701-020-00328-6

Cited by 10 publications

(4 citation statements)

References 40 publications

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“…This influence of the circulation of the magnetic potential on the eigenvalues evokes the Aharonov-Bohm effect. It has already been mentioned in [13], for more details on this phenomenon see the original reference [1], for a new point of view see also [2]. This result highlights some phenomena that should also appear in doubly connected case (without symetry) and in multiconnected domains.…”

Section: Introductionsupporting

confidence: 58%

Semiclassical spectrum of the Dirichlet–Pauli operator on an annulus

Bon

2022

Journal of Mathematical Physics

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This paper is devoted to the semiclassical analysis of the spectrum of the Dirichlet–Pauli operator on an annulus. We assume that the magnetic field is strictly positive and radial. We give an explicit asymptotic expansion at the first order of the lowest eigenvalues of this operator in the semiclassical limit. In particular, we exhibit the Aharonov–Bohm effect that has been revealed, for a constant magnetic field, in a recent paper by Helffer and Sundqvist.

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Section: Introductionsupporting

confidence: 58%

Semiclassical spectrum of the Dirichlet–Pauli operator on an annulus

Bon

2022

Journal of Mathematical Physics

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“…This debate is currently unsettled. Many papers have addressed this debate [43,44,45,46,47,48,49,50,51,52] and proposed other models that intend to explain the AB effect [53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76]. This debate may be naturally translated to the case of the AB effect involving a vector potential outside a closed flux line and a magnetic field confined along this closed flux line.…”

Section: A-explanation Vs B-explanation: Local and Nonlocal Interpret...mentioning

confidence: 99%

The Aharonov-Bohm effect in a closed flux line

Heras

2022

Preprint

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The Aharonov-Bohm (AB) effect was convincingly demonstrated using a microsized toroidal magnet but it is almost always explained using an infinitely-long solenoid or an infinitely-long flux line. The main reason for this is that the formal treatment of the AB effect considering a toroidal configuration turns out to be too cumbersome. But if the micro-sized toroidal magnet is modelled by a closed flux line of arbitrary shape and size then the formal treatment of the AB effect is exact, considerably simplified, and well-justified. Here we present such a treatment that covers in detail the electromagnetic, topological, and quantum-mechanical aspects of this effect. We demonstrate that the AB phase in a closed flux line is determined by a linking number and has the same form as the AB phase in an infinitely-long flux line which is determined by a winding number. We explicitly show that the two-slit interference shift associated with the AB effect in a closed flux line is the same as that associated with an infinitely-long flux line. We emphasise the topological nature of the AB phase in a closed flux line by demonstrating that this phase is invariant under deformations of the charge path, deformations of the closed flux line, simultaneous deformations of the charge path and the closed flux line, and the interchange between the charge path and the closed flux line. We also discuss the local and nonlocal interpretations of the AB effect in a closed flux line and introduce a non-singular gauge in which the vector potential vanishes in all space except on the surface surrounded by the closed flux line, implying that this vector potential is zero along the trajectory of the charged particle except on the crossing point where this trajectory intersects the surface bounded by the closed flux line, a result that questions the alleged physical significance of the vector potential and thereby the local interpretation of the AB effect.

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“…Thereby, the short-distance cutoff guarantees that the spectrum of energy is finite [3,4]. In recent decades, the attractive inverse-square potential has been studied through the Efimov effect [5], the generalized uncertainty principle [6], the electric dipole system in a (2+1)-dimensional conical spacetime [7] and the Aharonov-Bohm effect [8]. This singular potential has also been studied from the interaction of atoms with a ferromagnetic wire [9] and from the interaction of the permanent magnetic dipole moment of a neutral particle with a magnetic field [10].…”

Section: Introductionmentioning

confidence: 99%

On the attractive inverse-square potential in the induced electric dipole system under the influence of the harmonic oscillator

Bakke¹,

Ramos²

2022

EPL

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We obtain the analytical solutions to the Schr\"odinger equation for the the attractive inverse-square potential in an induced electric dipole moment system under the influence of the harmonic oscillator. We show that bound states can exist when the electric field configuration brings a cut-off point that imposes a forbidden region for the neutral particle. Then, by dealing with $s$-waves, we obtain the energy eigenvalues in the strong electric field regime and for small values of the angular frequency of the harmonic oscillator. Further, we extend our discussion about the energy eigenvalues beyond the $s$-waves.

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A New Version of the Aharonov–Bohm Effect

Cited by 10 publications

References 40 publications

Semiclassical spectrum of the Dirichlet–Pauli operator on an annulus

Semiclassical spectrum of the Dirichlet–Pauli operator on an annulus

The Aharonov-Bohm effect in a closed flux line

On the attractive inverse-square potential in the induced electric dipole system under the influence of the harmonic oscillator

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