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Saturday, September 27, 2008


The search for gravity goes on. With the Hadron supercollider shutdown till spring, the Higgs mechanism is in hibernation. The graviton is even more elusive. Is it hiding in the Klein Gordon Propagator and Spin Connections in Tangled Qubits populating the valleys of Spacetime?

Monday, September 22, 2008

Spin and Valleys In Graphene

It seems like a fun puzzle how these diagrams fit into the spin network boundaries of graphene. Can you imagine leptons as being these changing weaves that transform through the topology of the phase transitions of the valleys and 2-branes. What do you think Archimedes, Gauss and Grothendieck would make of this?

A Picture Worth a Thousand Words

The current issue of the Notices of the American Mathematical Society has handwritten diagrams by Archimedes and Alexander Grothendieck.

Wednesday, September 17, 2008

My Joke for Today

If this is not your cup of tea, then go out and find your own picture. The important thing is that you laugh each day!

The Dream of Graphene

Graphene has a significance that transcends its field of application. It provides the promise of creating sensors that actually image the force fields that make up our environment, as well as, molecular and particle detectors. People see in graphene a dream. It is a possible way to transcend the blindness of our technology and our painful ignorance of our environment.

Today’s technology does allow the construction rudimentary electromagnetic sensors and associated signal processing capability. The “spin filters” in the disk drive of current day laptop computers are only ones that people are generally aware of. This is seen as the starting point of where technology could go. Graphene provides not only a variety of for constructing such spin filters, but allows the possibility of other types of sensors, such as electrostatic, thermodynamic, etc.

Spin filters are constructed out of more primitive devices that can be fabricated from graphene. These include nanodisks, quantum dots, functionalized subwavelength quantum dots, etc. Using valley filters provides a sensor in the electrostatic domain complementary to the electromagnetic ones. Similarly, the techniques of electron counting spectroscopy permit the construction of probes to explore thermodynamic properties, such as thermal gradients and other statistical properties leading to the construction of motors controllable on a subnanometer scale, etc. In summary, graphene provides the new types of devices needed to construct sensors, processors, and a radical new type of technology.

Friday, September 5, 2008

Definition of Graphene

Definition of Graphene: Graphene is a 2-brane which anchors a triangular lattice of quarks whose vertices represent virtual locations or density of states characteristic of carbon atoms. Superimposed on this 2-brane is its chiral complement in which the triangles are rotated 180 degrees and moved, so that, each overlapping pair of triangles forms a Star of David. Sigma orbitals link the 2-branes together in a honeycomb arrangement. Pi orbitals with two valleys form like spouting mushrooms above and below the 2-brane. This permits Cooper pairs since they are time reversed electron states. The characteristic rippled shape of graphene means that the Fourier transform looks like a hexagon with light cones at the vertices rather than the cylinders it would have, if you could populate it in completely flat form. The properties of graphene are highly variable depending on how the 2-brane is populated internally and on the boundaries.
The total magnetic moment of graphene is zero when there are equal numbers of carbon atoms in its 2-brane and chiral complement. In the general case the total magnetic moment is half the difference between the numbers of atom populating the 2-branes. The magnetization in a zigzag edge has ferromagnetic ordering on each edge, but anti-ferromagnetic coupling between the edges. A single layer of graphene under low magnetic field oscillations has a Berry phase of pi while two layer systems display a Berry phase of 2pi. Similarly, a single layer has almost negligible magnetoresistance, while more than one layer has more conventional properties. Two layer graphene is most notable with respect to its noise cancelling properties.
Internal and external migration of carbon atoms forming pentagons and heptagons can warp the shape of the 2-brane without affecting the threefold coordination of the carbon atoms.
When a single carbon atom is missing from an internal hexagon, the resulting pentagon has “weak” and “gravitational” effects:
1. It exchanges the amplitudes of the two lattices.
2. It exchanges the two Fermi points.
3. It induces a phase coupling proportional to the deficit angle.
4. It induces local (4nm) “gravitational” curvature in spacetime and thus in the sheet. Spin connections provide a generalization of gauge fields used to model spacetime.
The resulting heptagon is paired with a pentagon. The pair acts as a diplole. The pentagon attracts charge and the heptagon repels charge. The heptagon induces negative “gravitational” curvature.