Relativistic Analogues of the Aharonov-Bohm Effect and the Landau Quantization with the Lorentz Symmetry Violation Determined by Azimuthal Electric Fields and a Fixed Vector Field

We search for relativistic quantum phases for a Dirac neutral particle with a permanent magnetic dipole moment in the cosmic string space–time under the effects of the violation of the Lorentz symmetry. This general relativity background is built based on the modified Maxwell theory coupled to gravity. Hence, we analyze analogues of the scalar Aharonov–Bohm effect for neutral particles in two different scenarios of the Lorentz symmetry violation in the cosmic string space–time.

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Aharonov–Bohm effect in a Coulomb-type potential under the influence of a cutoff point

International Journal of Modern Physics A ◽

10.1142/s0217751x21501360 ◽

2021 ◽

pp. 2150136

Author(s):

K. Bakke

Keyword(s):

Electric Fields ◽

Bound States ◽

Energy Levels ◽

Bound State ◽

Cutoff Point ◽

Coulomb Type ◽

Bohm Effect ◽

Forbidden Region ◽

Aharonov Bohm ◽

Type Potential

We analyze the influence of a cutoff point on a Coulomb-type potential that stems from the interaction of an electron with electric fields. This cutoff point establishes a forbidden region for the electron. Then, we search for bound state solutions to the Schrödinger equation. In addition, we consider a rotating reference frame. We show that the effects of rotation break the degeneracy of the energy levels. Further, we discuss the Aharonov–Bohm effect for bound states.

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Effects of a Landau-Type Quantization Induced by the Lorentz Symmetry Violation on a Dirac Field

Advances in High Energy Physics ◽

10.1155/2020/4208161 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

R. L. L. Vitória ◽

H. Belich

Keyword(s):

Vector Field ◽

Energy Levels ◽

Lorentz Symmetry ◽

Nonrelativistic Limit ◽

Dirac Field ◽

Hard Wall ◽

Symmetry Violation ◽

Wall Potential ◽

The Standard Model ◽

Massive Dirac Field

Inspired by the extension of the Standard Model, we analyzed the effects of the spacetime anisotropies on a massive Dirac field through a nonminimal CPT-odd coupling in the Dirac equation, where we proposed a possible scenario that characterizes the breaking of the Lorentz symmetry which is governed by a background vector field and induces a Landau-type quantization. Then, in order to generalize our system, we introduce a hard-wall potential and, for a particular case, we determine the energy levels in this background. In addition, at the nonrelativistic limit of the system, we investigate the effects of the Lorentz symmetry violation on thermodynamic aspects of the system.

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He–McKellar–Wilkens-type effect, quantum holonomies and Aharonov–Bohm-type effect for bound states from the Lorentz symmetry breaking effects

Reviews in Mathematical Physics ◽

10.1142/s0129055x16500239 ◽

2016 ◽

Vol 28 (10) ◽

pp. 1650023 ◽

Cited By ~ 2

Author(s):

A. G. de Lima ◽

H. Belich ◽

K. Bakke

Keyword(s):

Symmetry Breaking ◽

Bound States ◽

Energy Levels ◽

Lorentz Symmetry ◽

Standard Model Extension ◽

Symmetry Violation ◽

Gauge Sector ◽

Model Extension ◽

Lorentz Symmetry Breaking ◽

Aharonov Bohm

From the effects of the Lorentz symmetry violation in the CPT-even gauge sector of the Standard Model Extension determined by a tensor background [Formula: see text], we establish a possible scenario where an analogue of the He–McKellar–Wilkens effect can stem from. Besides, we build quantum holonomies associated with the analogue of the He–McKellar–Wilkens effect and discuss a possible analogy with the geometric quantum computation. Finally, we investigate the dependence of the energy levels on the He–McKellar–Wilkens geometric phase induced by Lorentz symmetry breaking effects when the particle is confined to a hard-wall confining potential.

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Phenomena and devices at the quantum scale and the mesoscale

10.1093/oso/9780198759874.003.0003 ◽

2017 ◽

Author(s):

Sandip Tiwari

Keyword(s):

Coulomb Blockade ◽

Secure Communication ◽

Quantum Hall ◽

Nanoscale Device ◽

Self Energy ◽

Stability Diagrams ◽

Charge Stability ◽

Bohm Effect ◽

Aharonov Bohm ◽

Non Locality

Unique nanoscale phenomena arise in quantum and mesoscale properties and there are additional intriguing twists from effects that are classical in origin. In this chapter, these are brought forth through an exploration of quantum computation with the important notions of superposition, entanglement, non-locality, cryptography and secure communication. The quantum mesoscale and implications of nonlocality of potential are discussed through Aharonov-Bohm effect, the quantum Hall effect in its various forms including spin, and these are unified through a topological discussion. Single electron effect as a classical phenomenon with Coulomb blockade including in multiple dot systems where charge stability diagrams may be drawn as phase diagram is discussed, and is also extended to explore the even-odd and Kondo consequences for quantum-dot transport. This brings up the self-energy discussion important to nanoscale device understanding.

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