Could quasi-periodic tilings play a part in High temperature Superconductivity ? Even in a heated disordered state, could the quasi-crystalline nature of the material enforce some kind of order wherein the global and local properties are interconnected ? Breaking this could possibly require very large amount of energy which could lead to a cooling of the system which could make the system amenable to the influence of electromagnetic fields which could lead to a disorder - order transition (associated with many phenomenon such as Bose Einstein Condensation, Superfluidity, Superconductivity etc) with associated dissipation of energy and further cooling.
Could the above play a part in diffractive rsdiative processes dominating over conductive diffusive processes ?? (Possibly through smooth but non-differentiable solutions of the associated transport equations due to singularities at multiple scales which could lead to localization). Could this be a mechanism for inducing superconductivity ? Could such fields / modes induce waveguides for photons / electrons / phonons and their bound states , especially through solitons etc ? And could this be related to superconductivity ??
Dear Sundaram,
The phase of wave function plays the vital role for arising Superconductivity.
Now it is a very common practice to develop single crystals.
Superconductivity arises when the phase symmetry is broken.
When the phase of each site of atoms add in an ordered manner , Superconductivity arises.
Then forming a single crystal of that type of Materials for which vibrational energy is very small and can't break the phase coherency at ambient temperature , that should, I think, show Superconductivity at ambient temperature .
If not, please discuss what parameters I am not including in my Discussion and what is wrong in my Discussion .
Best Wishes
Thanks
N Das
There is also the link between disorder and symmetry and order and symmetry breaking and with entropy and free energy. (Higher entropy -> Higher Symmetry - Higher degree of disorder -> Lower free energy).
Dear Sundaram,
The phase of wave function plays the vital role for arising Superconductivity.
Now it is a very common practice to develop single crystals.
Superconductivity arises when the phase symmetry is broken.
When the phase of each site of atoms add in an ordered manner , Superconductivity arises.
Then forming a single crystal of that type of Materials for which vibrational energy is very small and can't break the phase coherency at ambient temperature , that should, I think, show Superconductivity at ambient temperature .
If not, please discuss what parameters I am not including in my Discussion and what is wrong in my Discussion .
Best Wishes
Thanks
N Das
If 'quasiperiodic tilings' here can be understood as quasiperiodicity of the solid; then the existing framework of the theory of superconductivity will give different results without changing the basic notions.
DearSundaram Ramchandran,
As a general discussion on symmetry , entropy and disorder , I would like to request your opinion regarding the following.
A crystalline phase of a material is an ordered state , but the amorphous state is disordered state.
I mean , crystalline phase has less symmetry than the amorphous state.
But, for glass , as an example, the crystalline phase ( quartz ) is more stable than the amorphous state.
Can you please explain this in terms of order and disorder and entropy on this stability of phases ?
Thanks and Regards
N Das
I am a layman in this area but interested in these topics but my attempt to answer your question :
In glass, possibly, in the crystalline phase , there may be areas where there is local order interspersed with singularities / defects which possibly occurs at all scales and this possibly could lead to radiative / diffractive processes dominating over conductive /.diffusive processes leading to electron + photon + phonon (quartz is piezo-eletric) bound states and so the partial order in the crystalline phase is maintained by the electro-magnetic and acoustic modes which due to the partial order are coherent (as in a laser) and which stabilize the resonant crystalline (quasi-crystalline ??) modes against the modes that exhibit complete disorder where the acoustic and electromagnetic waves would be incoherent . This question also seems to shed "light" on the part that radiative processes can play in stabilizing ordered modes which could also play a part in high temperature superconductivity , laser cooling, superfluidity etc . Thanks for your question
Also, in relation to the above question, possibly entropy of (electrons + phonons + photons) >> entropy of electrons + entropy of phonons + entropy of photons (Superadditivity of entropy) , thus conferring stability on the crystalline / quasicrystalline bound modes. Another possibility is that the coherence in the collective motions / vibrations of the electrons / ions possibly leads to an increase in the number of separable , non-intersecting (orthogonal ??) trajectories / modes and hence in the entropy
Dear Sundaram,
probably, some of your questions can be answered in brief:
Superconductivity is a consequence of the local electron pairing and Bose-Einstein-Condensation of pairs as bosons.
This theoretical result is not surprising, since the local electrons can form singlet bonds with finite binding energies, whereas the Bose-Einstein-Condensation provides macroscopic non-dissipative fluctuations of condensed bosons.
Resistance and diamagnetic transitions at 286 K, found in Ag/Au nanostructures, quantitatively confirm the idea (for details see a comment https://arxiv.org/ftp/arxiv/papers/2001/2001.09752.pdf )
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