Fine Structure Constant from Graphene

Pi divided by the fraction of light transmitted through a single layer of graphene gives the reciprocal of the fine structure constant.

1. de Broglie wavelength of slow neutrons----------------137.03601082

2. AC Josephson effect in superconductor junction--------137.059770

3. Quantum Hall effect-----------------------------------137.0360037

4. Anomalous magnetic moment of electron---------------137.03599976

5. Anomalous magnetic moment of positron---------------137.03599976

6. Muonium atom----------------------------------------137.0359940

7. Helium spectrum--------------------------------------137.035853

8. Velocity of hydrogen 1s electron /velocity of light-------137.0388

(All values were obtained from book called "Hydrogen" published by Harvard University Press in 2002 by John S. Rigden)

Definition of the Meter

The latest in a long line of ways to determine the length of a meter is based on mode-locked femtosecond lasers and an optical frequency comb technique. A Nobel Prize was awarded in 2005 for this work.

Quantum Computers from Graphene

Researchers at the University of Leeds are looking for new ways to construct quantum computers using graphene.

The image below is an image of a magnetic field created by d-wave superconductivity.

There are various ways of creating the necessary double degeneracy for encoding a qubit.

D-wave superconductivity is being studied by IBM in thallium-copper-oxide high-temperature superconductors, as well as, in graphene. Below is a method of creating two Josephson junctions in single layer graphene. A gate voltage is used to tune either of the junctions to a pi phase. This pi phase regime implements the qubit.

In another variant, a d-wave Josephson junction could be tuned to create the doubly degenerate ground states. Other variants have also been by proposed by Guido Burkard's team at the University of Konstanz and others.

DNA Sequencing using Graphene

Artist's impression of a DNA molecule (helix) moving through a tiny slit in a graphene sheet (shown in blue). (Courtesy: Henk Postma).

Henk Postma at California State University Northridge has proposed a way of sequencing an entire DNA strand without the need for blasting or computer processing (arXiv:0810.3035v1 ).

Entangled Degrees of Freedom

Lepton pairs have degrees of freedom which are entangled or not.


Image copyright © Anton Zeilinger, Institute of Experimental Physics, University of Vienna.
Photon pairs are entangled in the illustration above.

Entangled particles fly apart in opposite directions.

Attempts are made to entangle the various degrees of freedom of various types of laser beams.

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The language seems sort of funny when you think of particles as brades. It seems natural they should get entangled. Nevertheless, it is really a degree of freedom that gets entangled between two entities like laser beams, allotropes, atoms, etc.

Gravity

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?

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.

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!