Aharonov-Bohm
Effect| Aharonov-Bohm
Effect |
In General > s.a. Aharonov-Casher
Effect;
geometric phase; locality;
topology in physics.
* Idea: The phase difference
= (e/
) 
between
the wave functions of two electrons going different ways around a line of magnetic
dipoles with magnetic flux .
* Significance: It
shows that, even if B = 0, in some non simply connected
region R, we cannot conclude that A = 0, because it 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.
References > s.a. charge [quantization]; non-commutative
geometry; Sagnac
Effect.
@
General references: Bohm & Aharonov PR(57);
Aharonov & Bohm PR(59);
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)
[
-function interaction];
Aharonov & Kaufherr PRL(04)qp;
Tiwari qp/04 [and
geometric phase]; Huérfano et al mp/07 [geometry];
de Oliveira & Pereira JSP(08)-a0810 [justification
of hamiltonian]; Batelaan & Tonomura PT(09)sep;
Sturrock & Groves a0910 [attribution to Ehrenberg and Siday].
@ 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 a0708 [macroscopic/classical
test]; Katanaev a0909 [geometrical].
@ 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).
@ Different particles
and backgrounds: Horner & Goldhaber PRD(97)
[for spin-1]; Alvarez JPA(99)
[on a cone]; 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].
@ 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 a0908 [in
a conical graphene sheet].
@ Related 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].
@ Variations: Holstein AJP(91)dec;
Franchini
& Golhaber PS(08)
[many vortices]; Jones-Smith et al a0911 [oscillating solenoid, radiation].
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5 nov 2009