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Quantum World Exhibits a Golden Ratio

February 2, 2010

Nanoscale symmetry exists in solid state matter. In fact, an international team of researchers claims that the signatures of that symmetry exhibit the same attributes as the golden ratio.

In order to study certain nanoscale quantum effects, Radu Coldea (Oxford University) and colleagues investigated cobalt niobate, which has magnetic properties. After they applied a magnetic field at right angles to an aligned spin, a magnetic chain became "quantum critical," which can be thought of as a quantum version of a fractal pattern.

By tuning the system and then introducing more quantum uncertainty, the researchers discovered that the chain of atoms acted like a nanoscale guitar string.

"Here the tension comes from the interaction between spins causing them to magnetically resonate," Coldea said. "For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618," he continued. That, it turned out, is the golden ratio.

Coldea said the finding "reflects a beautiful property of the quantum system--a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material."

The work, moreover, is another example of the way in which mathematical theory developed for particle physics has found an application in nanoscale science. "Such discoveries, said colleague Alan Tennant, "are leading physicists to speculate that the quantum, atomic scale world may have its own underlying order."

Coldea and colleagues summarized their findings in the article "Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry" (Science, January 8, 2010).

Source: (January 7, 2010)


Start Date: 
Tuesday, February 2, 2010