Talk:Magnetic flux quantum

Older Comments
Though the flux quantization was first discovered in superconductors, where current is carried by cooper pairs of charge 2e, the Aharonov-Bohm effect has been observed in many different, generally non-superconducting systems. The periodicity with the flux h/e in these systems is so general, that in many publications the flux quantum has been defined as $$ \Phi_0 = \frac{h}{e} $$.

The definition mentioned in the article is therefore just one of two existing conventions and may lead to confusion if taken for granted. To avoid this confusion, it might be helpful if the article at least mentioned the existance of these two different conventions.

The difference between the Dirac flux quantum and the superconducting flux quantum should indeed be clarified, as both definitions unfortunately use the same formula symbol. If you want a separate page for the Dirac flux quantum, this one should be renamed accordingly. However, I think we can cover both definitions on one page, as they are closely related and the entry is hardly in danger of becoming bloated.

Also, where exactly does the quoted value come from? The CODATA 2002 recommended value is 2.067 833 72(81) x10^-15 Wb, see, e.g. Mohr and Taylor, Rev. Mod. Phys 177:1-107. The one given here may well be more up to date, but without an attributable source and an error estimate that's of little value.Tim Stadelmann 22:50, 5 April 2006 (UTC)

Plank constant
The article should expressly address the 2*pi*h-bar = h notations, using one consistentlyLeadSongDog (talk) 22:25, 26 November 2007 (UTC)
 * Article is updated and uses only $h$ now. EdwardGoldobin (talk) 00:06, 29 January 2014 (UTC)

CGS versus SI Units
If a particle of charge q traverses a loop threaded by a magnetic field $$ \vec{B} $$, then its wavefunction will undergo a phase change of: $$ \exp\left( iq\int \vec{B}\cdot d\vec{(Area)}/\hbar c \right) =\int \exp\left( iq\vec{A}\cdot d\vec{x}/\hbar c \right) $$

When this phase change is unity, then the value of the flux is determined up to an integer: $$ \int \vec{B}\cdot d\vec{(Area)}= 2\pi N \hbar c/q $$

A universal definition of the flux quantum is therefore: $$ \Phi_0= 2\pi \hbar c/e $$

where e is the electron charge. In superconductivity applications the charge q is that of a Cooper pair and q=2e so one can also define: $$ \Phi_s= \pi \hbar c/e $$

Both definitions are in common usage.

In CGS units the universal flux quantum is: $$ \Phi_0= 2\pi \hbar/e = 4.1357\times 10^{-7} \; (gauss-cm^2) $$

and the superconductivity flux quantum is $$ \Phi_s= \pi \hbar/e = 2.0679 \times 10^{-7} \; (gauss-cm^2)$$

The ambiguity with electromagnetic units is that it involves both the issue of scales (length-time-mass), but also that of field normalizations. The fields appearing above are normalized either in the SI system or in the CGS system. This has really nothing to do with units, which is what confuses most people. We can equally well use a sensible system of units in which, eg., $$  \hbar = c=1 $$ and we use eV or GeV for all scales. We would still have to decide between the SI normalization vs. the Gaussian normalization.

In quantum field theory we define the Lagrange density as ($$ \hbar = c=1 $$ ): $$ \frac{1}{2}(\vec{E}^{2}-\vec{B}^{2}) - e\vec{A}\cdot J $$

which leads to the Maxwell equation: $$ \nabla\times\vec{B}-\partial_t \vec{E} = e\vec{ J} $$

This is a choice of canonical normalization of the fields. We can define a non-canonical normalization with the same $$ \hbar = c=1 $$  units: $$ \frac{1}{8\pi}(\vec{E'}^{2}-\vec{B'}^{2}) - e_{CGS}\vec{A'}\cdot J $$

which leads to the Maxwell equation: $$ -\partial_t \vec{E}-\nabla\times\vec{B} = 4\pi e_{CGS}\vec{ J} $$

The fields are related as: $$ \vec{E}=\vec{E'}/\sqrt{4\pi}\;\;\; \vec{B}=\vec{B'}/\sqrt{4\pi}\;\;\; \vec{A'}= \vec{A}/\sqrt{4\pi} $$

Now we restore $$\hbar,  c $$ and we can compute in Gaussian units (cm-gram-sec). When we see QFT equations with fields, Poynting vector, energy density, etc, we have to rescale by appropriate factors of $$ 1/4\pi $$. We often see QFT formulae written with $$ \alpha $$ and we have to then face the definition of the electric charge. In SI units the fine-structure constant is defined by $$ \alpha = e^2/4\pi \hbar c = (137.035999074(44))^{-1} $$

In CGS units we have $$ \alpha = e_{CGS}^2/ \hbar c = (137.035999074(44))^{-1} $$

so the electric charges are related as $$ e= e_{CGS}\sqrt{4\pi} $$

Note that in either case the interaction is the same: $$  e\vec{A}\cdot J = e_{CGS}\sqrt{4\pi}\vec{A'}/\sqrt{4\pi}\cdot J = e_{CGS}\vec{A'}\cdot J $$.

We can freely evaluate any formula obtained in QFT in the more convenient Gaussian system by rescaling the fields to Gaussian normalization and wherever we see $$ \alpha $$ we substitute $$ \alpha = e_{CGS}^2/ \hbar c $$. Some care must be taken in expressions derived in QFT involving magnetic moments and anomalies when they are evaluated in CGS units.

IMO both Gaussian and SI units are archaic and inconvenient and should be phased out in favor of $$ \hbar = c=1 $$ and eV / GeV for scale.

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=================================================== I think we need to check the formulae and make a clear demarcation between SI units and CGS units. CGS units include the $$c$$ for the speed of light, whereas my understanding is that SI units omit the $$c$$ and absorb it in the difference between Webers and Oersteds. If I substitute the accepted approximate values h = 6.626e-34, e = 1.602e-19, c=3e8 into the formulae,

$$ \frac{h}{2 e} \simeq 2 \times 10^{-15} $$ $$ \frac{h c}{2 e} \simeq 6 \times 10^{-7} $$ The article states that the flux quantum is $$ \simeq 2 \times 10^{-15} \mathrm{Wb}$$, so using the second formula for defining it is inconsistent and confusing.

That is because you are using the SI value for the electron charge $$ e $$ in the above formula, instead of the Gaussian-CGS unit, the statCoulomb, value of the electron charge. In both systems the value of the flux quanta is the same up to a factor of 10^8, the SI unit of $$\mathrm{Wb}$$ replaced by the Gaussian-CGS units $$\mathrm{G}\cdot\mathrm{cm}^2$$. (For example, see Kittel, Marder, or Landau & Lifshitz.)--ChristopherGutierrez (talk) 18:49, 20 December 2009 (UTC)

Although it is correct to express KJ and KJ-90 in Hz/V, a more compact (and consistent, since Φ0 is in Wb) unit is the Wb-1.TAB (talk) 19:34, 14 October 2011 (UTC)

Hey guys. Your article is confusing and a mess. Why do I have to come over here to discover that the units commonly cited in physics books are not what you are using. Furthermore you don't say what e is anyplace. This is a poorly written article, as usual for wikipedia, and as a researcher I found it to be nearly useless for answering my questions. I hate wikipedia and the poor way you write physics articles.

To conclude you need a discussion of the units so that this topic makes sense. I don't have the time to sit down and figure it out for myself. That is why I use wikipedia. But as usual you don't help much in providing the needed answers. This article is a mess and needs a lot of work.

72.64.44.43 (talk) 00:32, 5 January 2012 (UTC)


 * Guys, the standard units are SI for many years already. Period. CGS is used only by some theory guys (other theorists use dimensionless=normalized units). Anyway CGS measures e.g. capacitance in cm. Okay, go to electronic shop and bring/buy the capacitance of 1cm! Good luck! ;-) EdwardGoldobin (talk) 00:12, 29 January 2014 (UTC)

Lede
" . . . passing through a superconductor?" or " . . . passing through a superconducting loop?"William Jockusch (talk) 14:14, 18 January 2013 (UTC)
 * I agree that this should be changed. I've done so. — Quondum 18:08, 18 January 2013 (UTC)

Remaining questions

 * I find the story that flux quantum can be precisely measured using Josephson effect strange. Usually, exact knowledge of flux quantum (via $h$ and $e$) from atomic physics allows to build Josephson voltage standard. Are there any other opinions? EdwardGoldobin (talk) 00:15, 29 January 2014 (UTC)