scholarly journals Aharonov–Bohm effect revisited

2015 ◽  
Vol 27 (02) ◽  
pp. 1530001 ◽  
Author(s):  
Gregory Eskin
Keyword(s):  
Quantum Mechanical ◽  
Scattering Problems ◽  
Seminal Paper ◽  
Inverse Boundary ◽  
Yang Mills ◽  
Different Types ◽  
Gravitational Analog ◽  
Bohm Effect ◽  
Inverse Boundary Value Problems ◽  
Aharonov Bohm

Aharonov–Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959.We consider different types of Aharonov–Bohm effects such as the magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schrödinger equations with Yang–Mills potentials, and the gravitational analog of AB effect.We shall describe different approaches to prove the AB effect based on the inverse scattering problems, the inverse boundary value problems in the presence of obstacles, spectral asymptotics, and the direct proofs of the AB effect.

Observation of a gravitational Aharonov-Bohm effect

Science ◽  
2022 ◽  
Vol 375 (6577) ◽  
pp. 226-229 ◽  
Author(s):  
Chris Overstreet ◽  
Peter Asenbaum ◽  
Joseph Curti ◽  
Minjeong Kim ◽  
Mark A. Kasevich
Keyword(s):  
Wave Packets ◽  
Gravitational Interaction ◽  
Large Mass ◽  
Mechanical Effect ◽  
Quantum Mechanical ◽  
Electron Wave ◽  
Rubidium Atoms ◽  
Quantum Mechanical Effect ◽  
Bohm Effect ◽  
Aharonov Bohm

Gravitational interference The Aharonov-Bohm effect is a quantum mechanical effect in which a magnetic field affects the phase of an electron wave as it propagates along a wire. Atom interferometry exploits the wave characteristic of atoms to measure tiny differences in phase as they take different paths through the arms of an interferometer. Overstreet et al . split a cloud of cold rubidium atoms into two atomic wave packets about 25 centimeters apart and subjected one of the wave packets to gravitational interaction with a large mass (see the Perspective by Roura). The authors state that the observed phase shift is consistent with a gravitational Aharonov-Bohm effect. —ISO

BRAID GROUPS, ANYONS AND GAUGE INVARIANCE

1991 ◽  
Vol 05 (10) ◽  
pp. 1649-1664 ◽  
Author(s):  
Yong-Shi Wu
Keyword(s):  
Mechanical Properties ◽  
Braid Group ◽  
Group Analysis ◽  
Braid Groups ◽  
Quantum Mechanical ◽  
The Novel ◽  
And Topology ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Nontrivial Topology

The structure of braid groups on topologically nontrivial surfaces is reviewed. The physical meaning of the braid relations and their implications on quantum mechanical properties of anyonic quasiparticles are discussed. These include not only the exotic statistics of anyons but also the Aharonov-Bohm effect for the anyons on a surface with holes. Several results on the novel properties of anyons or their states, which were previously derived by microscopic considerations, are reproduced by this seemingly kinematic and topology-dependent braid group analysis. It is suggested that in the thermodynamic limit, the global excitations in a system on a surface of nontrivial topology do not interfere with properties of local anyonic quasiparticles.

NOVEL INTERFERENCE EFFECTS IN MULTIPLY CONNECTED NORMAL METAL RINGS

1994 ◽  
Vol 08 (05) ◽  
pp. 301-310 ◽  
Author(s):  
A.M. JAYANNAVAR ◽  
P. SINGHA DEO
Keyword(s):  
Quantum Interference ◽  
Normal Metal ◽  
Quantum Mechanical ◽  
Small Field ◽  
Interference Effects ◽  
Multiply Connected ◽  
Small Magnetic Field ◽  
Metal Rings ◽  
Bohm Effect ◽  
Aharonov Bohm

We have investigated the magnetoconductance of a normal metal loop connected to ideal wires in the presence of magnetic flux. The quantum mechanical potential, V, in the loop is much higher than that in the connecting wires (V=0). The electrons with energies less than the potential height on entering the loop propagate as evanescent modes. In such a situation, the contribution to the conductance arises from two non-classical effects, namely, Aharonov-Bohm effect and quantum tunneling. For this case we show that, on application of a small magnetic field, the conductance initially always decreases, or small field magnetoconductance is always negative. This is in contrast to the behavior in the absence of the barrier, wherein the small field magnetoconductance is either positive or negative depending on the Fermi energy and other geometric details. We also discuss the possibility of a better switch action based on quantum interference effects in such structures.

scholarly journals FERMIONIC ZERO MODES IN SELF-DUAL VORTEX BACKGROUND

2005 ◽  
Vol 20 (39) ◽  
pp. 3045-3053 ◽  
Author(s):  
YONGQIANG WANG ◽  
TIEYAN SI ◽  
YUXIAO LIU ◽  
YISHI DUAN
Keyword(s):  
Phase Shift ◽  
Zero Mode ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Yang Mills ◽  
Zero Modes ◽  
Extra Space ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Unified Description

We study fermionic zero modes in the background of self-dual vortex on a two-dimensional non-compact extra space in 5+1 dimensions. In the Abelian Higgs model, we present a unified description of the topological and non-topological self-dual vortex on the extra two dimensions. Based on it, we study the localization of bulk fermions on a brane with the inclusion of Yang–Mills and gravity backgrounds in six dimensions. Through two simple cases, it is shown that the vortex background contributes a phase shift to the fermionic zero mode, this phase is actually origin from the Aharonov–Bohm effect.

scholarly journals Gravitational Dressing of Aharonov-Bohm Amplitudes

1997 ◽  
Vol 12 (06) ◽  
pp. 1043-1051 ◽  
Author(s):  
Giovanni Amelino-Camelia ◽  
Ian I. Kogan ◽  
Richard J. Szabo
Keyword(s):  
Three Dimensional ◽  
Matter Field ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Gravitational Analog ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Chern Simons

We investigate Aharonov-Bohm scattering in a theory in which charged bosonic matter field are coupled to topologically massive electrodynamics and topologically massive gravity. We demonstrate that, at one-loop order, the transmuted spins in this theory are related to the ones of ordinary Chern-Simons gauge theory in the same way that the Knizhnik-Polyakov-Zamolodchikov formula relates the Liouville-dressed conformal weights of primary operators to the bare weights of primary operators to the bare weights in two-dimensional conformal field theories. We remark on the implications of this connection two-dimensional conformal field theories and three-dimensional gauge and gravity theories for a topological membrane reformulation of strings. We also discuss some features of the gravitational analog of the Aharonov-Bohm effect.

Phenomena and devices at the quantum scale and the mesoscale

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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