Aharonov–Bohm superselection sectors

AbstractWe show that the Aharonov–Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the analysis of superselection sectors from Minkowski spacetime to an arbitrary globally hyperbolic spacetime unveils the presence of a new quantum number labelling charged superselection sectors. In the present paper, we show that this “topological” quantum number amounts to the presence of a background flat potential which rules the behaviour of charges when transported along paths as in the Aharonov–Bohm effect. To confirm these abstract results, we quantize the Dirac field in the presence of a background flat potential and show that the Aharonov–Bohm phase gives an irreducible representation of the fundamental group of the spacetime labelling the charged sectors of the Dirac field. We also show that non-Abelian generalizations of this effect are possible only on spacetimes with a non-Abelian fundamental group.

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Quantum interference in H + HD → H2 + D between direct abstraction and roaming insertion pathways

Science ◽

10.1126/science.abb1564 ◽

2020 ◽

Vol 368 (6492) ◽

pp. 767-771 ◽

Cited By ~ 8

Author(s):

Yurun Xie ◽

Hailin Zhao ◽

Yufeng Wang ◽

Yin Huang ◽

Tao Wang ◽

...

Keyword(s):

Quantum Number ◽

Quantum Interference ◽

Chemical Reactivity ◽

Rotational Quantum Number ◽

Interesting Case ◽

Phase Effect ◽

Chemical Reaction Dynamics ◽

Bohm Effect ◽

Aharonov Bohm ◽

Direct Abstraction

Understanding quantum interferences is essential to the study of chemical reaction dynamics. Here, we provide an interesting case of quantum interference between two topologically distinct pathways in the H + HD → H2 + D reaction in the collision energy range between 1.94 and 2.21 eV, manifested as oscillations in the energy dependence of the differential cross section for the H2 (v′ = 2, j′ = 3) product (where v′ is the vibrational quantum number and j′ is the rotational quantum number) in the backward scattering direction. The notable oscillation patterns observed are attributed to the strong quantum interference between the direct abstraction pathway and an unusual roaming insertion pathway. More interestingly, the observed interference pattern also provides a sensitive probe of the geometric phase effect at an energy far below the conical intersection in this reaction, which resembles the Aharonov–Bohm effect in physics, clearly demonstrating the quantum nature of chemical reactivity.

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Topological quantum scattering under the influence of a nontrivial boundary condition

Modern Physics Letters A ◽

10.1142/s0217732316500747 ◽

2016 ◽

Vol 31 (11) ◽

pp. 1650074 ◽

Cited By ~ 4

Author(s):

Herondy Mota

Keyword(s):

Boundary Condition ◽

Phase Shift ◽

Gordon Equation ◽

Scattering Problem ◽

Quantum Scattering ◽

Topological Quantum ◽

Klein Gordon ◽

Bohm Effect ◽

Aharonov Bohm

We consider the quantum scattering problem of a relativistic particle in (2 + 1)-dimensional cosmic string spacetime under the influence of a nontrivial boundary condition imposed on the solution of the Klein–Gordon equation. The solution is then shifted as consequence of the nontrivial boundary condition and the role of the phase shift is to produce an Aharonov–Bohm-like effect. We examine the connection between this phase shift and the electromagnetic and gravitational analogous of the Aharonov–Bohm effect and compare the present results with previous ones obtained in the literature, also considering non-relativistic cases.

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QUANTIZATION AND SUPERSELECTION SECTORS II: DIRAC MONOPOLE AND AHARONOV-BOHM EFFECT

Reviews in Mathematical Physics ◽

10.1142/s0129055x90000041 ◽

1990 ◽

Vol 02 (01) ◽

pp. 73-104 ◽

Cited By ~ 18

Author(s):

N.P. LANDSMAN

Keyword(s):

General Procedure ◽

Preceding Paper ◽

Quantum Effects ◽

Magnetic Monopoles ◽

Unitary Representations ◽

Dirac Monopole ◽

Topological Quantum ◽

Bohm Effect ◽

The Given ◽

Aharonov Bohm

The quantization procedure of the preceding paper is applied to study two generic topological quantum effects, viz. the charge quantization induced by (abelian) magnetic monopoles, and the Aharonov-Bohm effect. Prior to these applications, a general procedure is given for reducing unitary representations of a locally compact G which are induced by nontrivial unitary representations of H⊂G. This involves the use of spherical trace functions, and is useful in the determination of the eigenfunctions of the Hamiltonian of the particle in a given superselection sector. Such Hamiltonians, implementing the time-evolution on the given abstract C*-algebra, are explicitly constructed and analyzed. The relevant quantum effects are found to be a consequence of the representation theory of the appropriate algebras of observables. In this way a group- and operator-theoretic elucidation of the mathematical structure of the given systems is attempted. This paper may be read independently of its predecessor.

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L-DEPENDENCE OF PARTICLE RADIATION IN MAGNETIC-SOLENOID FIELD AS AHARONOV-BOHM EFFECT

International Journal of Modern Physics A ◽

10.1142/s0217751x02010480 ◽

2002 ◽

Vol 17 (06n07) ◽

pp. 1045-1048 ◽

Cited By ~ 5

Author(s):

V. G. BAGROV ◽

D. M. GITMAN ◽

V. B. TLYACHEV

Keyword(s):

Magnetic Field ◽

Charged Particle ◽

Quantum Number ◽

Radiation Intensity ◽

Radiation Spectrum ◽

Semiclassical Approximation ◽

Particle Radiation ◽

Bohm Effect ◽

Aharonov Bohm ◽

Azimuthal Quantum Number

Aharonov-Bohm solenoid changes the energy spectrum of charge particles in pure magnetic field. In particular, the degeneracy with respect to azimuthal quantum number l is partially lifted. In turn, this complicates the radiation spectrum of a charged particle in magnetic field in the presence of the solenoid (Aharonov-Bohm effect). In particular, the degeneracy of the radiation intensity with respect to the azimuthal quantum number is lifted completely. In the present work we study l-dependence (induced by Aharonov-Bohm solenoid) of synchrotron radiation intensity in semiclassical approximation.

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Maxwell Electrodynamics in Terms of Physical Potentials

Symmetry ◽

10.3390/sym11070915 ◽

2019 ◽

Vol 11 (7) ◽

pp. 915 ◽

Cited By ~ 3

Author(s):

Parthasarathi Majumdar ◽

Anarya Ray

Keyword(s):

Maxwell Equations ◽

Minkowski Spacetime ◽

Laplacian Operator ◽

Charged Scalar ◽

Gauge Invariant ◽

Vector Potentials ◽

Maxwell Electrodynamics ◽

Gauge Fixing ◽

Bohm Effect ◽

Aharonov Bohm

A fully relativistically covariant and manifestly gauge-invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge-invariant potentials without entailing any gauge fixing. We show that the inhomogeneous equations satisfied by the physical scalar and vector potentials (originally discovered by Maxwell) have the same symmetry as the isometry of Minkowski spacetime, thereby reproducing Einstein’s incipient approach leading to his discovery of special relativity as a spacetime symmetry. To arrive at this conclusion, we show how the Maxwell equations for the potentials follow from stationary electromagnetism by replacing the Laplacian operator with the d’Alembertian operator, while making all variables dependent on space and time. We also establish consistency of these equations by deriving them from the standard Maxwell equations for the field strengths, showing that there is a unique projection operator which projects onto the physical potentials. Properties of the physical potentials are elaborated through their iterative Nöther coupling to a charged scalar field leading to the Abelian Higgs model, and through a sketch of the Aharonov–Bohm effect, where dependence of the Aharonov–Bohm phase on the physical vector potential is highlighted.

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Aharonov-Bohm Effect for Bound States on the Confinement of a Relativistic Scalar Particle to a Coulomb-Type Potential in Kaluza-Klein Theory

Advances in High Energy Physics ◽

10.1155/2015/925846 ◽

2015 ◽

Vol 2015 ◽

pp. 1-6 ◽

Cited By ~ 13

Author(s):

E. V. B. Leite ◽

H. Belich ◽

K. Bakke

Keyword(s):

Bound States ◽

Scalar Potential ◽

Scalar Particle ◽

Minkowski Spacetime ◽

Klein Theory ◽

Coulomb Type ◽

Bohm Effect ◽

Aharonov Bohm ◽

Type Potential ◽

Kaluza Klein

Based on the Kaluza-Klein theory, we study the Aharonov-Bohm effect for bound states for a relativistic scalar particle subject to a Coulomb-type potential. We introduce this scalar potential as a modification of the mass term of the Klein-Gordon equation, and a magnetic flux through the line element of the Minkowski spacetime in five dimensions. Then, we obtain the relativistic bound states solutions and calculate the persistent currents.

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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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