The Aharonov–Bohm effect is a quantum mechanical phenomenon in which an electrically charged particle is affected by a non-zero electromagnetic gauge potential despite there being a zero electromagnetic field (in the region where the particle is allowed to propagate). This coupling results in the particle's wavefunction to gain a phase factor, and hence is most noticeable in interference experiments.
Questions tagged [aharonov-bohm]
46 questions
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Local explanation of the Aharonov-Bohm effect in terms of force fields
Here is an interesting paper for the Physics SE community:
On the role of potentials in the Aharonov-Bohm effect. Lev Vaidman. Phys. Rev. A 86 no. 4, 040101 (R) (2012). arXiv:1110.6169 [quant-ph].
You should check it out because it's an amusing…
Mark Mitchison
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What is the conclusion from Aharonov-Bohm Effect?
What is the conclusion that we can draw from the Aharonov-Bohm effect? Does it simply suggest that the vector potential has measurable effects? Does it mean that it is a real observable in quantum mechanics? Does this effect has anything to do with…
SRS
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What is the analog of the Aharonov-Bohm effect for general gauge fields and for gravity?
The Aharonov-Bohm effect concerns the electromagnetic fields, where a quantum particle can feel the effect of an electromagnetic field in regions where it vanishes, through the electromagnetic potential 4-vector $A_\mu$.
What is the analog of this…
TheQuantumMan
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Aharonov-Bohm using density matrix?
On the one hand, we know that the overall phase of the wave function (of the whole system) is not a measurable quantity, but more an artifact of mathematical description — the physical states are rays in the Hilbert space. The description in terms…
mavzolej
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Is it possible to derive the Aharonov-Bohm effect using translation operators alone?
There are multiple proofs of the Aharonov-Bohm effect. Arguably the most simple proof is the original one by Aharonov and Bohm which appears to be proven by inspection. Two other methods I have seen use the machinery of the Berry phase and the path…
Hermitian_hermit
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Is the magnetic vector potential "real" in classical electromagnetism?
From how I've learned it in school the magnetic vector potential is used as a mathematical tool to simplify problems with current-carrying wires in classical electromagnetism, but is never treated as bearing any physical meaning. After doing some…
Lambda
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Aharonov-Bohm Effect Interaction Energy Interpretation: $\vec E_m = -∇Φ - D\vec A/Dt$?
The Wang paper "An experimental proposal to test the physical effect of the vector potential" proposes an experiment to decide between two interpretations of the Aharonov-Bohm effect:
“the interpretation of electromagnetic potentials”
or
“the…
James Bowery
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A theoretical issue in the mathematical description of the Aharonov-Bohm experiment
Mathematically viewing, the Aharonov-Bohm experiment shows that the magnetic field creates a connection with a nonzero holonomy on a multiply-connected domain. This means that there isn't a state function that is continuous on that domain. This…
mma
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Deriving the non-abelian Aharonov-Bohm effect as a Berry phase
I am trying to derive the non-abelian Aharonov-Bohm effect by generalising Michael Berry's derivation to the case of non-abelian gauge field $A$.
My derivation so far
We require a degenerate eigenspace in order to achieve a non-abelian Berry phase…
Hermitian_hermit
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Reference request for the Aharonov-Bohm effect
I am looking for a good reference to an online source or book, on the magnetic Aharonov-Bohm effect. I have read the appropriate sections from the book by Griffiths and Ballentine, and still haven't understood it properly. The reference should also…
user7757
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Aharonov-Bohm effect and periodic boundary conditions for particle on a ring
For a particle on a ring, we have the periodic boundary conditions $\psi(\phi+2\pi)=\psi(\phi)$. If we also have a magnetic field penetrating perpendicularly the ring, then when the particle goes around the ring once, it picks up an Aharonov-Bohm…
TheQuantumMan
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Is special relativity falsified by the Aharonov-Bohm effect?
The Lorenz gauge is the only Lorentz invariant electrodynamic gauge. If the vector potential has physical meaning, as in the Aharonov-Bohm effect (ABE), then the gauge condition can not be arbitrarily chosen and Lorentz invariance seems gone.
How…
David Jonsson
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Could a delayed choice Aharonov-Bohm experiment be used for FTL information transfer?
Tim Maudlin about a delayed choice Aharonov-Bohm experiment, the section between 1:35:00 and 1:38:30
In the interview above Tim Maudlin mentions some sort of delayed choice Aharonov-Bohm experiment. He considers a double slit experiment with…
Cristian Dumitrescu
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Can the Aharonov-Bohm experiment also be described by conditional probablilties, like the simple double slit?
The most attractive description of the double slit experiment for me is that in Beltrametti and Cassinelli's book.$^{[1]}$ The essence of their description is the following.
Beltrametti-Cassinelli description of the double-slit experiment - They…
mma
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What would it mean for Aharanov-Bohm effect in a gauge in which the vector potential vanishes everywhere outside the solenoid?
Is it possible to find a gauge in which the vector potential outside the solenoid (with axis along $z$-axis) is made equal to zero everywhere? If so, wouldn't the phase difference in the Aharanov-Bohm experiment be equal to zero in that gauge when…
Solidification
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