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David
“Golden ratio” hints at hidden atomic symmetry
Jan. 7, 2010
Courtesy Helmholtz Association
of German Research Centres
and World Science staff
A hitherto undiscovered symmetry can be found in solid matter at very small scales, physicists are reporting. The symmetry, they say, involves the golden ratio famous from art and architecture.
Particles at the atomic, or quantum, scale behave in unexpected and seemingly irrational ways. New properties emerge that stem from an effect known as Heisenberg’s Uncertainty Principle.
The researchers in the new study focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains like a very thin bar magnet, but only one atom wide. They are considered a useful model for describing magnetism at tiny scales in solid state matter.
When a magnetic field is applied to the chain at right angles to an aligned “spin” of its particles, the magnetic chain transforms into a new state called quantum critical, according to the physicists. This can be thought of as a quantum version of a fractal pattern, a pattern that looks the same at any scale.
Such a state is also a type of “quantum uncertain” or “Schrödinger cat” state, in which certain properties of the particles are indeterminate, said Alan Tennant of the Helmholtz Center Berlin for Materials and Energy, one of the researchers.
By tuning the system the researchers found that the chain of atoms acts like a guitar string whose tension comes from interaction between the spins of the constituent particles. “For these interactions we found a series,” or “scale,” of “resonant notes,” said Radu Coldea of Oxford University, who led the research.
“The first two notes show a perfect relationship with each other,” added Coldea, principle author of a paper on the findings to appear in the Jan. 8 issue of the research journal Science.
The “pitch” of these notes, or their frequencies of vibration, are in a ratio of about 1.618, the same “the golden ratio famous from art and architecture,” he continued. If two numbers are related by the golden ratio, their sum is also related to the larger of them by the golden ratio. In other words, if A divided by B is that special number, then A+B divided by A is the same number.
Artists and architects have have used the golden ratio for centuries—for example, rectangles 1.618 times higher than they are wide—because it supposedly provides esthetically pleasing forms. The golden ratio is irrational, like pi, meaning its decimals go on forever.
In the “quantum uncertain” state of matter, the ratio “reflects a beautiful property of the quantum system – a hidden symmetry,” Coldea said. It is “actually quite a special one called E8 by mathematicians, and this is its first observation in a material.” The findings dramatically illustrate how mathematical theories developed for particle physics may find application in science at the nanoscale—the scale of a few atoms—and ultimately in future technology, he added.
“Such discoveries are leading physicists to speculate that the quantum, atomic- scale world may have its own underlying order,” said Tennant. “Similar surprises may await researchers in other materials in the quantum critical state.”
The researchers reached their results by using a special probe called neutron scattering that allows physicists to see the atomic-scale vibrations of a system. “Using neutron scattering gives us unrivalled insight into how different the quantum world can be from the everyday,” said researcher Elisa Wheeler, who has worked at both Oxford and the Berlin center on the project.
Particles at the atomic, or quantum, scale behave in unexpected and seemingly irrational ways. New properties emerge that stem from an effect known as Heisenberg’s Uncertainty Principle.
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Diagram of the neutron scattering technique used in the experiments. The arrows represent the spin axes of particles in the linked chain of atoms. A magnetic field is used to tune the chains of spins to a "quantum critical" state. The resonant modes (“notes”) are detected by scattering neutrons, which are beamed at the setup in the direction shown. While passing through the system, these scatter with the characteristic frequencies of the spin chains. (Credit: Tennant |
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When a magnetic field is applied to the chain at right angles to an aligned “spin” of its particles, the magnetic chain transforms into a new state called quantum critical, according to the physicists. This can be thought of as a quantum version of a fractal pattern, a pattern that looks the same at any scale.
Such a state is also a type of “quantum uncertain” or “Schrödinger cat” state, in which certain properties of the particles are indeterminate, said Alan Tennant of the Helmholtz Center Berlin for Materials and Energy, one of the researchers.
By tuning the system the researchers found that the chain of atoms acts like a guitar string whose tension comes from interaction between the spins of the constituent particles. “For these interactions we found a series,” or “scale,” of “resonant notes,” said Radu Coldea of Oxford University, who led the research.
“The first two notes show a perfect relationship with each other,” added Coldea, principle author of a paper on the findings to appear in the Jan. 8 issue of the research journal Science.
The “pitch” of these notes, or their frequencies of vibration, are in a ratio of about 1.618, the same “the golden ratio famous from art and architecture,” he continued. If two numbers are related by the golden ratio, their sum is also related to the larger of them by the golden ratio. In other words, if A divided by B is that special number, then A+B divided by A is the same number.
Artists and architects have have used the golden ratio for centuries—for example, rectangles 1.618 times higher than they are wide—because it supposedly provides esthetically pleasing forms. The golden ratio is irrational, like pi, meaning its decimals go on forever.
In the “quantum uncertain” state of matter, the ratio “reflects a beautiful property of the quantum system – a hidden symmetry,” Coldea said. It is “actually quite a special one called E8 by mathematicians, and this is its first observation in a material.” The findings dramatically illustrate how mathematical theories developed for particle physics may find application in science at the nanoscale—the scale of a few atoms—and ultimately in future technology, he added.
“Such discoveries are leading physicists to speculate that the quantum, atomic- scale world may have its own underlying order,” said Tennant. “Similar surprises may await researchers in other materials in the quantum critical state.”
The researchers reached their results by using a special probe called neutron scattering that allows physicists to see the atomic-scale vibrations of a system. “Using neutron scattering gives us unrivalled insight into how different the quantum world can be from the everyday,” said researcher Elisa Wheeler, who has worked at both Oxford and the Berlin center on the project.
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