Correlated delocalized electrons in band structure is entanglement.  Band theory already has this built in.  

I think No!, The quantum entanglement for two particles forms a closed Hamiltonian system, i.e. the spatial variation of the total energy of the two entangled particles maintains to be zero, dE/dr =0; there is no force between the two entangled particles. So there is nothing to do with enhancing the material properties by the electrons. Even they are entangled, there is No force! The force perhaps only acts as destroying factor to their quantum entanglement.

The main problem about building a quantum computer is that entanglement is extremely fragile. The slightest termal noise will destroy entanglement. Therefore various other effects will completely dominate except if the system is isolated from the rest of the world.

What is thought important in the cohesion of metals

is a proportion of conduction electrons which move throughout

the metal. These are states of the whole metal chunk, so have much lower energy than states related to atoms. This energy gain stabalizes the material.

This is the usual thought. I cannot confirm or rule out a posible role of entangled states.

Correlated delocalized electrons in band structure is entanglement.  Band theory already has this built in.  

I think No too, i have the same answer of Zhizhong Yan.

good luck Mourik

It is not only the band structure that involves entanglement, but actually the electromagnetic interaction in general is based on momentum entangled multi-particle states. In Feynman's formulation of QED, this entanglement is 'caused' by the exchange of 'virtual quanta' (of momentum). Today we call it 'exchange of gauge bosons', but mathematically it is still the same as in Feynman's seminal papers of 1949/50.

Basically, entanglement is an inherent property of two-particle states that are correlated by a given (and fixed) total momentum and orbital angular momentum (cf. arXiv:1604.05965). This kind of entanglement is by no means 'extremely fragile', because it is nothing other than the electromagnetic interaction.

P. Van Mourik's question is about entanglement of non-valance electrons. If these were entangled they would interact electromagnetically and we would call then valance electrons. Hence, by definition, non-valance electrons are not (momentum) entangled. 

Not sure why Walter is stuck on "momentum entangled".  The electron-electron interaction is (of course) very powerful so the band structure is highly dominated by it.  Basically, if your state is not a (anti)symmetrized product of one particle states, it is entangled.  

Hi,

On a larger scale, there are so-called shape memory alloys. I checked to see how it was related to thermal expansion,  but this is both ways. In material science it is called dislocations.

Formed plastic cups contracts subjected to heat (boiling water) into original small oblate shape. But it is not electrons, or is it?, it is elongated molecules or chains of molecules with stored energy, that relax when heated.

Lena, yes.  It is like Shrinky Dinks!  The plastic stores the memory in its stress.  I think NiTinol might be the same.  As a superelastic material it can deform far without introducing new defects.

I see. Before reading your comment, I was about to add that; it could be that it copies the shape and more dense structure of the bottom in the boiler vessel, but likely not.

Rubber, also shows interesting features. For these materials (not metals), are there atom fine scale?

@Clifford:

I just wanted to make sure which kind of entanglement we are talking about. Zhizhong Yan seems to have spin entanglement in mind. I am talking about ‘momentum entanglement’, which is synonymous for ‘virtual exchange of momentum’, which in QED ‘causes’ the interaction. My point is that a two-particle eigenstate of total and orbital angular momentum must be momentum entangled because of the commutation relations of the Poincare group. In other words, interaction is an intrinsic property of two-particle states in relativistic quantum mechanics.

Walter,

QED is kind of overblown as an explanation.  Technically one can argue that everything electromagnetic is "QED" but we usually only pull out that bat when we are talking about particle creation as a necessary component of the effect.  Here, electrostatics is all that is required.  

There group theoretical arguments are also unnecessary.  It is simply a high dimensional space (Fock space) that has ground state solutions that don't factor - as is typical.  

Clifford,

P.'s question was about entanglement between two (or more) non-valence electrons, not about valence electrons. Therefore, I tried to explain what entanglement means in this context. I do not consider this as overblown.

In fact it is very simple: If two particles are considered as a closed (isolated) system, they have conserved total and angular momenta. A two-particle state with well-defined quantum numbers of total and angular momentum cannot be an eigenstate of the individual particle momenta at the same time. (Here the group theoretical argument is necessary.) This means that the two-particle state must be momentum entangled. Momentum entanglement defines a correlation between two electrons that can be understood (mathematically described) as the result of an exchange of quanta of momentum between the electrons. (If you like, you may use the notion of 'particle creation' in this context.) Exchange of quanta is another wording for interaction. In contrast to the standard formulation of QED, the coupling constant of this interaction can be calculated from group theoretical relationships: it is identical to the electromagnetic fine-structure constant. You may answer the question for yourself, whether or not this is only a technical argument.

Dear Contributors to this discussion,

As a non-expert in this field of solid state physics, I'am highly impressed by the relevant answers to my original question. Thank you all! May I make the following remarks hoping to see them be corrected in case necessary?

*The metal band structure or electron communism can be conceived as quantum entanglement of the metal valency electrons.

*In a metals the non-valency electrons are in general in larger numbers present than the valency electrons, this seems especially true for the engineering metals. In case these non-valency electrons do not show any interaction with non-valency electrons in neighbouring grains, does that mean that their contributions on e.g. the atomic forces (elastic constants) are theoretically zero?

At last I like to add some background to my original question. The values of the elastic metal constants largely depend on the interatomic forces within the metals, e.g. alloying a metal within the limits of solid solution only slightly changes the Young's Modulus. Therefore elastic constants are generally regarded as intrinsic properties. The metal strength is in fact determined by dislocation movement possibilities: grain size, precipitates, lattice transformations, alloy compositions, work hardening. So metal strength is generally regarded as an extrinsic property. Hence I was just wondering if some interaction by the majority of the electrons in a metal at such short distances as across grain boundaries could contribute to elastic constants as well to metal strength with possibly remarkable engineering consequences.

@Walter,

I am familiar with the language you are using.  Many people are not aware that they are speaking in a model dependent picture of band and MO theory - not the true general reality of QM.  The real physical object is the 3N dim wavefunction with its associated symmetries and spinor labels.  It is the former picture that makes entanglement look like something special or important.  The distinction of "valence" electron is such a model dependent statement.  

We like to use the one particle pseudo Hamiltonian picture because it is intuitive and convenient in some cases but it is a bit of a tortured fiction.  Diagrammatic QFT encourages this picture but the founders knew it was a fiction and just a computational tool that needed such language as a conversational shortcut.