A New Version of the Aharonov–Bohm Effect

@article{deOliveira2020ANV,
  title={A New Version of the Aharonov–Bohm Effect},
  author={C{\'e}sar R. de Oliveira and Renan G. Romano},
  journal={Foundations of Physics},
  year={2020},
  volume={50},
  pages={137-146}
}
We propose a simple situation in which the magnetic Aharonov–Bohm potential influences the values of the deficiency indices of the initial Schrödinger operator, so determining whether the particle interacts with the solenoid or not. Even with the particle excluded from the magnetic field, the number of self-adjoint extensions of the initial Hamiltonian depends on the magnetic flux. This is a new point of view of the Aharonov–Bohm effect. 
View on Springer
arxiv.org
7 Citations
Background Citations
2

7 Citations

Citation Type

Citation Type

Aharonov–Casher effect in the presence of spin-dependent potential
Semiclassical spectrum of the Dirichlet–Pauli operator on an annulus
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…
Semiclassical spectrum of the Dirichlet-Pauli operator on an annulus
. 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…
The Aharonov–Bohm effect in a closed flux line
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…
Potential Fields in Fluid Mechanics: A Review of Two Classical Approaches and Related Recent Advances
The use of potential fields in fluid dynamics is retraced, ranging from classical potential theory to recent developments in this evergreen research field. The focus is centred on two major…
Inverse-square-type potential from the interaction of the magnetic quadrupole moment of a neutral particle with a magnetic field
Three dimensional Green function in cylindrical coordinates: application to the Aharonov–Bohm effect of double arc-slits

References

SHOWING 1-10 OF 46 REFERENCES
Aharonov-Bohm Effect with $δ$--type Interaction
A quantum particle interacting with a thin solenoid and a magnetic flux is described by a five-parameter family of Hamilton operators, obtained via the method of self-adjoint extensions. One of the…
On the Aharonov–Bohm Hamiltonian
Using the theory of self-adjoint extensions, we construct all the possible Hamiltonians describing the nonrelativistic Aharonov–Bohm effect. In general, the resulting Hamiltonians are not…
Mathematical Justification of the Aharonov-Bohm Hamiltonian
It is presented, in the framework of nonrelativistic quantum mechanics, a justification of the usual Aharonov-Bohm hamiltonian (with solenoid of radius greater than zero). This is obtained by way of…
Can elementary quantum mechanics explain the Aharonov–Bohm effect?
It is shown that a satisfactory treatment of the Aharonov–Bohm problem requires no departure from the basic principles of ordinary quantum mechanics, a fact not entirely clear in the literature. The…
Macroscopic test of the Aharonov-Bohm effect.
TLDR
The observation of the absence of time delays associated with forces of the magnitude needed to explain the AB-phase shift for a macroscopic system is reported.
Aharonov-Bohm effect in bound states: Theoretical and experimental status
The Aharonov-Bohm effect has recently been questioned on theoretical and experimental grounds. Such discussins have suffered from ambiguities which resulted from their focusing on scattering states.…
Aharonov-Bohm scattering of a wave packet of finite extension
The scattering of an electron from a thin, shielded solenoid (Aharonov-Bohm effect) is studied by means of the time-dependentGreen's function of the problem. The structure of theGreen's function…
Elastic scattering and bound states in the Aharonov-Bohm potential superimposed by an attractive ρ-2 potential
We consider the elastic scattering and bound states of charged quantum particles moving in the Aharonov-Bohm and an attractive ?-2 potential in a partial-wave approach. Radial solutions of the…
Scattering and self-adjoint extensions of the Aharonov-Bohm hamiltonian
We consider the hamiltonian operator associated with planar sec- tions of infinitely long cylindrical solenoids and with a homogeneous magnetic field in their interior. First, in the Sobolev space…
Experimental test for approximately dispersionless forces in the Aharonov-Bohm effect
A new class of forces, approximately dispersionless forces, were recently predicted as part of a semiclassical description of the Aharonov-Bohm effect. Electron time-of-flight measurements have been…
...
...