Noncommutative Graphene as quantum entanglement in Gyroid Solar Cells

So the basic model is noncommutative phase as creating quantum nonlocal entanglement - or the two as one.

The entanglement criterion for continuous variable systems and the conditions under which the uncertainty relations are fulfilled are generalized to the case of a noncommutative phase space. The quantum nature and the separability of noncommutative two-mode Gaussian states are examined. It is shown that the entanglement of Gaussian states may be exclusively induced by switching on the noncommutative deformation.

The point being this noncommutative phase is what the ancients knew already and practiced as macroquantum alchemy. This philosophy is either practiced or not understood - in other words to try to explain it in words, leads to confusion for most. But Graphene as a material - embodies this secret.

 we conclude that our method of introducing noncommutative coordinates provides another formulation of the confined massless Dirac fermions in graphene.

And so it is shown that noncommutative phase is (2018) actually a more accurate analysis and description of Graphene: (pdf)
 


 So this brings us back to solar cells and graphene: vid lecture

We discuss the classical and non-commutative geometry of wire systems which are the complement of triply periodic surfaces....In this setting the gyroid geometry can be seen as the 3d generalization of graphene.

 https://www.technologyreview.com/s/603445/graphene-goes-3-d/

Imagine a twisted honeycomb. But instead of a bunch of different sides all stuck together, Buehler explains that it only has two sides that fold over one another repeatedly.

"The surface in this gyroid is continuous," Buehler says. "So if you look at a small piece, it's always two-dimensional. It's always perfectly connected. But if you zoom out, it forms a three-dimensional structure, so you can build things with them."

 http://www.wbur.org/news/2017/02/17/mit-graphene-structure

  In this new material, electrons could move in all 3 directions, acting as if they had no mass.

 John Baez on Gyroid Graphene

In nature, self-assembled gyroid structures are found in certain surfactant or lipid mesophases^[6] and block copolymers. In the polymer phase diagram, the gyroid phase is between the lamellar and cylindrical phases. Such self-assembled polymer structures have found applications in experimental supercapacitors,^[7] solar cells^[8] and nanoporous membranes.^[9]
Gyroid membrane structures are occasionally found inside cells.^[10]

 https://en.wikipedia.org/wiki/Gyroid

 The gyroid is the most interesting case in its geometry and properties as it exhibits Dirac points (in 3d). It can be seen as a generalization of the honeycomb lattice in 2d that models graphene. Indeed, our theory works in more general cases, such as periodic networks in any dimension and even more abstract settings. After presenting our theoretical results, we aim to invite an experimental study of these Dirac points and a possible quantum Hall effect. The general theory also allows to find local symmetry groups which force degeneracies aka level crossings from a finite graph encoding the elementary cell structure.

Theoretical Properties of Materials Formed as Wire Network.... Available from: https://www.researchgate.net/publication/324681346_Theoretical_Properties_of_Materials_Formed_as_Wire_Network_Graphs_from_Triply_Periodic_CMC_Surfaces_Especially_the_Gyroid

 So it's a noncommutative torus...also found in proteins...

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Gyroid on Youtube

Causality and Noncommutativity, Andrzej Sitarz on youtube