Fraction Quantum Hall Effect

[elas]

'The enigmatic electron' by McGregor deals extensively with the various ways of measuring electron radius.

'Composite fermions' by Jain shows what can be done by distorting the shape.

 

'The ideas of particle physics' by Coughlan, Dodd and Gripaios. and 'Facts and mysteries in Elementary particle physics' by Veltman give a clear explanation of current knowledge.

 

I do not think Bertrand Russell would make the same statement today.

[swansont]

The electron is not a composite fermion.

[elas]

The electron is not a composite fermion.

 

Agreed but Jain makes it quite clear that at the lower Landau level he is dealing with single electrons, not composite fermions. Jain also states that in order to include single electrons in the current FQHE theory, it is necessary to move into three dimensions (current composite fermion work is two dimensional), something that is proving difficult to achieve with any degree of accuracy.

 

This means that the observed (single electron) fractions (1/3, 1/5, and 1/7) are but one measurement of three possible measurements. As proposed elsewhere, it is an interpretation of all the observed fractional sequences that is needed in order to see the three dimensional electron.

 

It is also worth noting that Jain states that single electrons have different energies at different Landau levels; if the electrons are passing through the experimental equipment at the same velocities (Jain does not make this clear) then the properties of (Jain's) electrons are not constant unless a structural formula is used to explain the different energies.

 

In order to encourage a substantial debate the point raised above is explained in detail as follows:

 

Extract from ‘Composite Fermions’ by Jainendra K. Jain

 

….when the filling factor is an interger (v = 1) the ground state is especially simple N electrons occupy N single particle orbitals

 

It is clear from the above (and many other similar statements) that, at the lowest Landau level, Jain et al are referring to single electrons. The single electron fractions (N1) are given as 1/3, 1/5, 1/7, and 1/9. Jain refers to these fractions as approximations.

 

My table shows the exact fractions and approximations of all single electrons within the atoms of the elements. Graphs of the table are comparable with Fig. 2.5 of Jain’s book.

 

 

The following extract is from the introduction to the section on ‘Incompressible ground states’:

 

Unfortunately a comparison with real life experiments also necessitates an inclusion of the effects of nonzero thickness of the electron wave function, Landau level mixing, and disorder, which are not well understood as the FQHE, and the accuracy of quantitive comparisons between theory and experiment is determined largely by the accuracy with which these other effects can be incorporated into the theory. (roughly within a factor of 2; but occasionally 10-20%).

 

Atoms, of course; have non-zero thickness and the conversion of resistance to compression into ‘Landau’ levels is simply a matter of converting actual fractions into Jain’s approximate fractions as shown in the diagram above.

 

An extract from J.K. Jain / Physica E 20 (2003) 79-88 reads:

 

The composite fermion itself is an exceedingly complicated object from the electrons’ point of view, because the quantized vortex, one of its constituents, is a collective entity in which all electrons participate.

 

I have often thought that charge is the ratio of the ‘elastic force of matter’ to the ‘vacuum force of the particle field’. The extract from Jain’s paper allows a clear definition of charge as follows:

 

Charge = Elasticity of matter/vacuum force

 

In the diagram below, 2/3 of the electrons’ matter is transferred to the vortex but, the vacuum force (being the properties of the electron vacuum zero point) is not transferable. It follows that if we consider only the portions either side of the vortex we have 1/3 of the elastic force of matter, and all of the vacuum force and an therefore a 1/3 fractional charge but, if we consider the whole electron (i.e. including the portion of matter in the vortex [according to Jain]) then we observe all the matter and its elasticity to give a charge of 1.

 

The vortex force can be separated as a single entity creating a virtual particle; the matter is re-absorbed by the electrons that may change particle states as a result of the action.

 

 

The table taken from Heseilberg’s paper can now be reduced to:

 

 

The maximum field overlap is the distance between particle centers (vacuum zero points).

Edited June 13, 2008 by elas
multiple post merged

[swansont]

The point this turns into a CLF discussion is where it gets moved to speculations. You want to try again?

[elas]

The point this turns into a CLF discussion is where it gets moved to speculations. You want to try again?

 

I took the submission to the speculations forum and removed all reference to CLF.

 

At one point Jain questions whether nature has an equivalent action to FQHE, I have tried to point out that each atom is a compression chamber, a spherical version of the FQHE. I cannot understand which portion you are objecting to but, if you will state which portion needs removing I will do so.

 

Perhaps I should put it this way - if I had written the above before coming up with the CLF model would it have been regarded as speculative?

Edited June 13, 2008 by elas

[elas]

Further to the above, the following table brings together all the different fractional sequences that have been submitted at various times in the past.

 

Perhaps the real value of the table is that it proposes a simple calculation for finding the width of the spin (or vortex) particle. Taken together with the compression diagram, the table also explains why fractionally charged particles are not observed in experiments specically designed to detect fractionally charged particles. It is because the fractional charge is only a semi-detached part of the whole particle; similar to a quark and its gluon.

Edited June 16, 2008 by elas
multiple post merged

[swansont]

Perhaps I should put it this way - if I had written the above before coming up with the CLF model would it have been regarded as speculative?

 

That would depend on how you defined/explained ‘elastic force of matter’ and ‘vacuum force of the particle field,’ among other things.

 

DO NOT answer this here.

[elas]

swansont

 

I need to understand at what point theoretical physics becomes speculative. For example:

fractions of shell electrons do not extend beyond 1/5; if I propose that 1/4, 1/3 and 1/2 are 1s (i.e. nuclear electron) fractions and extend that to propose that the nucleus has a value of 1: is it theory or speculation.