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I was reading about nanopartilces(NPs) and their properties. At several places I have read that NPs act as coherent body. I wonder if the Nps can be treated as Bose Einstein condensate (BEC) as suggested here. NPs have a crystal structure which suggest that NPs are more like a solid (condensed matter) and the same is suggested by several books on NPs. BEC is formed at ultra low temperature hence apparently there is no link between NPs and BEC. However can the coherent nature of NPs be associated with the of coherence of BEC.

thanks in advance

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    $\begingroup$ What does 'a coherent body' mean? Basically the nuclei are extremely correlated (trivially because they are in a lattice), I would guess that this prevents formation of BEC, but I am not qualified enough on BEC to state this formally. $\endgroup$
    – Mikael Kuisma
    Commented May 6, 2016 at 13:18
  • $\begingroup$ Bose-Einstein Condensate is first of all a state of matter where a significant number of particles have dropped to zero energy level and thus doesn't contribute thermodynamically and appears as if number of particles isn't conserved. This is only possible for Bosonic matter, obeying Bose Einstein statistic. So the first question I guess would be: are those nano-particles Bosonic? $\endgroup$
    – Ilya Lapan
    Commented May 6, 2016 at 20:28
  • $\begingroup$ @Ilya Lapan For the sake of arguments let us say they are Bosonic $\endgroup$
    – hsinghal
    Commented May 6, 2016 at 20:58
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    $\begingroup$ I don't think you can just assume that they are bosonic. We are talking about some sort of crystal structure, that means they are made of a nucleus (protons, neutrons) and electrons, the ordinary matter basically. Electrons are definitely fermions, obey Pauli exclusion principle and can't drop out into the lowest state. The nucleus, on the other hand, can be a boson, depends on what particles it is made of. Helium-4 is a boson for example. So, with a non-interacting mix of bosons and fermions you would find that the bosons condense out and fermions stack up on energy levels. $\endgroup$
    – Ilya Lapan
    Commented May 6, 2016 at 23:06
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    $\begingroup$ So what you get would not resemble anything you initially started with. Bu here we are talking about interacting particles (you did mention lattice,right?). So this makes the whole thing a lot more complicated. But the feeling I get is that a Bose-Einstein condensate would be very far from a lattice of some nanoparticles. I find it very hard imagining a lattice of particles acting in such a way, with the number of particles not being conserved and all of that.But again, I am not entirely sure what are those particles you are talking about. $\endgroup$
    – Ilya Lapan
    Commented May 6, 2016 at 23:12

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After discussion with my colleagues what I understood is

If the material is cooled down (to nano kelvin) the wave function of the atom (mainly nuclei) is spread and it got overlapped with neighboring atoms.

If the number of atoms within this coherent volume is larger than one (and the atom is a boson i.e. total angular momentum of nuclei and electrons is an integer) then it will form a Bose-Einstein Condensate (BEC).

Due to the overlap of the nuclei wave functions the individuality of the nuclei is lost and the surrounding electron cloud could not distinguish among the nuclei and all the electrons will make a common electron cloud among coherently connected nuclei. Hence the atoms as a whole act as single entity.

On the other hand in case of nanoparticles (NPs) the outer electron has sufficiently low energies such that their wave functions overlap and make a common electron cloud. However the inner electron cloud and nuclei remain separated from each other and maintain their individuality.

The two situations are quite different hence NPs possess coherency on the scale of low energy electrons but a NP is certainly not a BEC.

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