Aharonov-Bohm Effect  

In General > s.a. Aharonov-Casher Effect; geometric phase; locality in quantum mechanics; topology in physics.
* Idea: The phase difference Δφ = (e/\(\hbar\)) Φ between the wave functions of two electrons going different ways around a line of magnetic dipoles with magnetic flux Φ; It was actually proposed by Ehrenberg and Siday years before the work by Aharonov and Bohm.
* Significance: It shows that if in some non-simply-connected region R the magnetic field B = 0 we cannot conclude that A = 0, because A is a connection, and this has physical effects beyond the presence of forces.
* Potential vs field: If one wants to obtain it as a local interaction of the electron current with something, then one has to use the vector potential A; But the effect can be explained as an interaction of the electron's magnetic field inside the solenoid with the other magnetic field, without using As at all (Ó Raifeartaigh).
* Remark: It can be obtained for any theory of particles coupled to a connection, including gravity, with conical singularities.
@ General references: Ehrenberg & Siday PPS(49); Bohm & Aharonov PR(57); Aharonov & Bohm PR(59), PR(61); Merzbacher AJP(62)apr; Peshkin PRP(81); Peshkin & Tonomura 89; Holstein CP(95); Magni & Valz-Gris JMP(95); Adami & Teta LMP(98)qp/97 [Hamiltonians]; Dabrowski & Stovícek JMP(98) [δ-function interaction]; Aharonov & Kaufherr PRL(04)qp; de Oliveira & Pereira JSP(08)-a0810 [justification of hamiltonian]; Batelaan & Tonomura PT(09)sep; Sturrock & Groves PT(10)apr-a0910 [attribution to Ehrenberg and Siday]; Eskin a1007 [simple proof]; Dennis et al ed-JPA(10) [50 years]; Dulat & Ma PRL(12)-a1203; Hiley a1304 [early history, before Aharonov and Bohm]; Pearle & Rizzi a1507 [inclusion of the source], a1605 [three alternative views].
@ Geometric: Tiwari qp/04 [and geometric phase]; Huérfano et al IJTP(07)mp.
@ Wave function: Alvarez PRA(96); Berry & Shelankov JPA(99); Richard a0811 [expressions for wave operators]; > s.a. representations in quantum mechanics.
@ Interpretation: Belot BJPS(98) [repercussions]; Blanco FP(99) [no classical interpretation]; Boyer FP(00), FP(00), FP(02); Costa de Beauregard FP(04) [and measurement of A]; Mattingly SHPMP(06) [gauge matters]; Caprez et al PRL(07)-a0708, comment Ivezić a1407 [macroscopic/classical test]; Katanaev RPJ(11)-a0909, RPJ(11)-a1212 [geometrical]; Peshkin JPA(10)-a1009 [against a proposed local explanation]; Fearn & Nguyen a1104-conf [using classical forces]; Vaidman PRA(12)-a1110, comment Aharonov et al PRA(15)-a1604 [on the role of potentials]; Kowar a1111 [causal explanation in non-instant field model of electrodynamics]; Vaidman fs(14)-a1301 [paradoxes, locality and entanglement]; Wallace a1407; Boyer wd-a1408 [classical electromagnetic force]; Batelaan & Becker a1507 [loopholes].

Related Topics > s.a. charge [quantization]; Sagnac Effect.
@ Experiments: Werner & Brill PRL(60) [theoretical]; Chambers PRL(60) [confirmation]; Boyer FPL(06) [and forces]; Caprez et al PRL(07) [showing absence of forces]; Byer FP(08); Laganá a1403 [spectroscopic version].
@ On a cone: Alvarez JPA(99); Sitenko & Vlasii JPA(10)-a1002 [and short-wavelength scattering limit]; Andrade et al PRD(12), a1207 [for spin-1/2 particle].
@ Different particles and backgrounds: Horner & Goldhaber PRD(97) [for spin-1 fields]; Spavieri PRL(99) [with electric dipole]; Sjöqvist AQC(04)qp/03 [molecular]; Horsley & Babiker PRA(08) [role of internal degrees of freedom]; Buniy & Kephart PLA(09) [knotted magnetic solenoid].
@ Electric field version: Walstad IJTP(10)-a1607; Weder JMP(11)-a1006; Walstad a1607/IJTP.
@ Gravitational analog: Bezerra JMP(89); Harris AJP(96)apr [for photons]; Tartaglia gq/00 [and lensing]; Barros et al MPLA(03); Marques & Bezerra PLA(03), MPLA(04); Heller et al IJTP(08); Fonseca et al PLA(10)-a0908 [in a conical graphene sheet]; Hohensee et al PRL(12)-a1109 [force-free gravitational redshift]; Chiao et al fs(15)-a1301; Nouri-Zonoz & Parvizi PRD(13)-a1306 [effects of Gaussian curvature].
@ Other topics: Dowling et al PRL(99) [and similar phases]; Aguilar & Socolovsky IJTP(02) [and Green's theorem]; Furtado & Duarte PS(05) [dual]; Dragoman & Bogdan qp/05 [in momentum space]; Nesterov IJGMP(07) [and non-associative, path-dependent wave functions]; Sitenko & Vlassi a1005, AP(11) [quasiclassical limit].
@ And covariance / Lorentz invariance: Singleton & Vagenas PLB(13)-a1305 [covariant generalization]; Kang a1308 [fully relativistic treatment].
@ Other variations: Holstein AJP(91)dec; Franchini & Golhaber PS(08) [many vortices]; Jones-Smith et al PRD(10)-a0911 [oscillating solenoid, radiation]; Fang et al PRL(12) [for photons, from a harmonically modulated refractive index]; Chiao a1206 [ferromagnetic core covered with a superconducting material]; > s.a. diffraction; non-commutative geometry.


main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 22 jul 2016