Globally stationary but locally static space-times: A gravitational analog of the Aharonov-Bohm effect

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.

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Gravitational Dressing of Aharonov-Bohm Amplitudes

International Journal of Modern Physics A ◽

10.1142/s0217751x97000773 ◽

1997 ◽

Vol 12 (06) ◽

pp. 1043-1051 ◽

Cited By ~ 3

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.

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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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