Aharonov-Bohm Effect| 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 PRA(17)-a1507 [inclusion of the source],
PRA(17)-a1605 [three alternative views];
Franklin AJP(19)aug [non-locality of magnetic field effect];
Das Gupta a2010-ch.
@ 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];
Saldanha FP(21)-a1910 [local description].
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 IJTP(17)-a1607.
@ 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];
de Oliveira & Romano FP(20)-a2002 [magnetic flux and self-adjoint extensions of the Hamiltonian].
@ 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.
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