Dear Prof. Lugovoi,

                                  I will give you an Econophysics explanation to your computation and this is derived from my paper on Political Enviornment and String Theory published on my RG page as well as my HAAG's Theorem paper. The answer is that because of Maxwell's Laws of magnetic and electric fields which are linear and curls the electron will be drawn towards the atom whose atomic distance is less interpolated by the random electron spin by transferring the negative charge.This is my Econophysics answer. Earl Prof. Dr SKM QC EPS Fellow (In) MES MRES MAICTE

Dear Soumitra K Mallick,

Thank you for answer.

     However,

I need to get precise numbers , namely, space distribution of magnitude of magnetic field and the orientation of vector of magnetic field, if the origin of that field is only magnetic moment of ion.

Dear Profs. Lugovoi and Kapusta,

                                   I am sorry but I am not mentally ill but possibly quite exhausted , I have been publishing one way or the other since 1987 and in many fields like Commerce, Management,  Game Theory, General Equilibrium Theory, Stock Markets, Banking Sector, Information Technology, Growth Theory, Quantitative Finance, Mathematical Finance, General Physics, String Theory, Internet Physics (implicitly). Physics for Education and also Genetic Algorithms, Coal Mining and Econophysics. I have publications listed on the Research Gate website. I have developed the systems approach to String Theory with Econophysics experiments and now I am trying to answer the question, in what ways is the Econophysics Field of lower dimension than the Astrophysical Field of course by using my Econophysics String theoretic Stock Market experiments. I hope you change your mind and please take a look at my publications if you will. I believe there are fundamental unifying scientific principles between cybernetic systems like InterNetworked Stock and Banking Markets on Earth and Astrophysical Systems.which satisfy the Anthropic Principle and the Arrow of Time besides the postulate of growing Entropy. But at the cost of perhaps angering everybody (I am humbled by the prospect) I have to provide an explanation for the Uniform Closure properties of Earth Based Cybernetic Systems connected by the internet and Energy conservation Laws. So I am moving to that questionnaire I am trying to find it. As things stand these are also my publications if the profession agrees. I am an indirect Fellow of the European Physical Society. Thanks for caring, Sir. Earl Prof.  SKM QC D.Phil. EPS Fellow (In) MRES MES MAICTE

We are all exhausted by informational explosion, Soumitra. Don't try to follow informational flows, but try to think independently.

Good question, Vladimir, What is magnetic field? (More precisely, electromagnetic)

Scattering of conductivity electrons on magnetic impurities is Kondo effect (or problem). It is a good problem. In your case scattering on charge will dominate.

To use formula 44.4 You must know perfectly your distances. Conductivity electron is quasi-particle. Where is it located?

Happy new year to all!

Eugene.

Eugene,

In the theoretical paper [http://dx.doi.org/10.4236/jmp.2015.67103]  it was obtained condition for the formation of the energetically favorable filamentary quantum structures (for example, built of conductivity electrons). Each structure is described by of one wave function, that is, the electrons are indistinguishable (up to the moment when we shall have destroyed structure).

The phrase "energetically favorable" is decisive in the choice of the direction of movement for all processes in physics  (the variational principle).

So we just need to find some similar conditions, and nature itself will begin to create energetically favorable structure.

A phrase "similar conditions" means some approximation in the coordinate of conductive electron when we use (44.4) (see description of my question).

A phrase "quasi-particle" looks like some approximation in the coordinate.

Thus, we seems can take 10^{-8} cm as some approximation in the coordinate of electron.

Now about scattering of conductivity electrons on magnetic impurities.

In paper [http://dx.doi.org/10.4236/jmp.2015.67103], it was obtained that the magnetic field can create electron structures. Therefore, any changing of magnetic field can change, create or break a quantum structure. Thus, a question arises  :   What is magnetic field?  (we have conductive electron and ion which have charges, magnetic moments and movement concerning each other …   And I do not try to calculate a simple scattering. I need to take into account only a correct magnetic field.)

 Still not sure to get your question, Vladimir.

Formula 44.4 is the field generated by a magnetic dipole moment \vec(m) located at the origin. If the moment can be regarded as fixed in orientation and magnitude, then so os the dipole moment vector and you can straightworwardly go on computing the field at any location in space based on this formula. [You will have to get unit conversions right. 1 Bohr magneton is 9.274E-24 J/T or 9.274E-24 Am2]

There is still an approximation, though: if the source of the magnetic moment is not a "point dipole" but of finite extension, then the formula describes this dipolar field only for sufficiently large distances, well above the characteristic length scale of the magnetic object. In case of an atom or ion, the characteristic length scale will be of the order of a few Angstroms.

But then, if what you want to describe is the effect of a magnetic ion onto a conduction electron, things probably really are more intricate. If we talk about conduction electrons then you probably deal with some kind of a solid. now, also in the Fe ion/atom, electrons are the source of the magnetic moment. So, unless any form of exchange mechanism is suppressed, it will be the major source of interaction (e.g. leading to the Kondo interaction mentioned by Eugene, or RKKY interaction between different Fe atoms/ions etc etc). For the most part, we generally neglect the influence of the dipolar field in solids but for considerations of shape anisotropy. And even here, we usually consider magnetization itself as a vector field and do not take its granularity (short length scale fine structure) into account. [se discussion of fields on different length scales in Jackson's electrodynamics].

Does this help at all??

Kai, Eugene, thanks, situation has became more clear for me.

However, I can not find a theoretical paper where the magnitudes (and directions) of magnetic field (of ion for electron of conductivity) are calculated.

Let me question:

is there Kondo effect in two-dimentional physics ?

Seems, ion of Fe destroys superconductivity , whereas ion of alkali metals (potassium K etc.) promotes an appearance of superconductivity (for example, superconductive fullerene K_{3}C_{60} , whereas C_{60} is not superconductor). At first sight, the reason here is the difference in magnetic properties of Fe and K.

Allow us to be interested not in the energy interaction between the ion and the electron of conductivity , but in magnetic field, which has effect on the electron of conductivity, and so, determines the properties of electron of conductivity. Eugene stressed that electron of conductivity is a composite particle. However, composite particle is a result of some (not strong) interaction. It's like we have some instant structure, and magnetic field of ion has essential influence on this instant structure. Magnetic field could be our sensor (perhaps more than sensor...). So, what is that magnetic field?

You don't need a theoretical paper to calculate the dipolar field of an ion. You simply take the formula and do it. Of course, that is the far field. If you want the near field, then you would have to calculate the spatial spin (and orbital current) densities and calculate the field by integrating over the atomic volume.

Nevertheless I don't think that is meaningful (I may be wrong, of course). The dominant interaction will be an exchange interaction. This is also a reason why magnetic impurities pose a danger for superconductivity. (Unless we have a situatin where magnetic fluctuations might actually contribute to the SC mechanism. You will know that this is being discussed analogously for high TC  superconductors as well as heavy fermion systems, because there are similarities in their generic phase diagrams.)

Magnetically there is of coursa a huge difference between Fe and K, when it comes to magnetism. K has essentially one valence electron, which easily donated to the system. So if you think of the K sites as K+ ions (ionic limit) then there are no partialy filled shells and hence no magnetic moment. In contrast, the partially filled 3d shell in Fe shall always prevail and unless there is a strong crystal field forcing a zero spin ground state, the intra-atomic interactions will try to establish a magnetic moment on the Fe site.

I don't see how the magnetic field would be a sensor?!??

For the additional question of whether there can be a Kondo effect in 2D the answer is YES, imho.

(As a matter of fact, the [single impurity] Kondo propblem is inherently a one-dimensional one, since all interactions occur in symmetry adapted fashion, i.e. a projection of the conduction states onto the impurity orbital symmetry happens automatically.

In the standard formulation, s-wave scattering is assumed (i.e. hybridization/scattering occurs with the l=0 partial waves of the Fermi sea). If the local scatterer is a d or f state, it happens just with another partial wave. This is then called Coqblin-Schrieffer model. For single electron local occupancy, the Kondo effect happens in the same way regardless which partial wave needs being considered. In case of large degenceracy (>2), the full theory gets complex in the latter case, however [e.g. Andrei & Lowenstein, 1983; Schlottman 1983, 1984]).

Edit: and  let me add (again): the key to Kondo physics is exchange interaction, not the dipolar field of the impurity. How could one try to understand this, even though the local field might be "not so small"? In doing Kondo physics you consider the effect of having a spatially local interaction involving spin (and hence the Pauli principle). This affects the many body states directly (since we are dealing with fermions) not just their energetics. A magnetic field just changes the energy expectation value (to first order) of the single particle (basis) states. If the field is localized, the change of (the expectation value of the) energy of a strongly delocalized (Bloch) state is next to negligible.

                      Thanks for understandable and clear description.

Well, dominant interaction will be an exchange interaction.

An exchange interaction opens a direct way to Kondo effect.

However, why is not there (experimentally observed) Kondo effect for the two-dimension graphene?

         (if I don't miss information)

Moreover, for the phenomena of SC, a collective behaviour of conductive electrons , their long-distance strong correlation, seems, could not be occur at short-distance exchange interaction.

   So, pheraps, the other physics has to be.

landau levels ( in transverse magnetic field) can create (minimal) energetically favorable state for eache electron of conductivity.

If we have electrons of conductivity, we have positive ions which lost of them.

(in the system of equal velocities) We have electrons and ions which move in opposite directions, so they create magnetic field each for other. Which field does help to occur SC and Which field does not help to occur SC ?

This point of view , seems, tells that

we should be able to calculate the correct magnetic field, which gives a decisive contribution . But what is it?

Graphene/graphite is not only essentially two-dimensional but there is very little density of states at the Fermi level (zero without doping). That is detrimental for the Kondo effect (check experessions for Kondo - J and/or TK in Hewson, Fazekas or other sources).

Kai is right, Vladimir. The key is exchange interactions. They can be not only short-distance, but also long-distance, for example through conduction electrons. Average magnetic field (we can speak only about average because conduction electrons are totally delocalized) does not help here.

In the case of graphene global theorems don't help. According to the global Landau theorem about order in two dimensions graphene can not exist at all. But it exists.

Happy new year!

Eugene.

Seems, in two-dimensional (like a graphene) flat surface, it could be formed one-dimensional, filamentary, long-range ordered structures, formed by any number of n of charged fermions (see red circles in added fig.1 from http://dx.doi.org/10.4236/jmp.2015.67103 ).

The properties of this structure are like the properties of condensate

(see added fig.2, where \Delta y_{n}  is the averaged distance between the particles in filamentary structure) : 

-  the linear density of particles (in filamentary structure) grows with the number (n) of particles of structure,    

- the linear density of particles (in filamentary structure) grows with the magnitude of external magnetic field ,

- energy per one electron of filamentary structure is reduced with growing number of n of electrons. 

One structure (with any fixed number of n of particles) is described by one wave function; therefore, the particles, which form structure, are indistinguishable. 

Could this be connected also and with exchange interaction? (Perhaps, with interaction between two filamentary structures, which are the same each other and have the same quantum nature …) Any opinions would be important for me.  Thanks.

Does exist magnetic momentum tables or figures for light ions? (in A*m2 or J/T)