[ExI] golden ratio discovered in quantum world

spike spike66 at att.net
Fri Jan 8 01:16:10 UTC 2010

Since we are discussing weirdness, check this:


Golden ratio discovered in a quantum world

Researchers from the Helmholtz-Zentrum Berlin für Materialien und Energie
(HZB, Germany), in cooperation with colleagues from Oxford and Bristol
Universities, as well as the Rutherford Appleton Laboratory, UK, have for
the first time observed a nanoscale symmetry hidden in solid state matter.
They have measured the signatures of a symmetry showing the same attributes
as the golden ratio famous from art and architecture.

The research team is publishing these findings in Science on the 8 January.

On the atomic scale particles do not behave as we know it in the
macro-atomic world. New properties emerge which are the result of an effect
known as the Heisenberg's Uncertainty Principle. In order to study these
nanoscale quantum effects the researchers have focused on the magnetic
material cobalt niobate. It consists of linked magnetic atoms, which form
chains just like a very thin bar magnet, but only one atom wide and are a
useful model for describing ferromagnetism on the nanoscale in solid state

When applying a magnetic field at right angles to an aligned spin the
magnetic chain will transform into a new state called quantum critical,
which can be thought of as a quantum version of a fractal pattern. Prof.
Alan Tennant, the leader of the Berlin group, explains "The system reaches a
quantum uncertain - or a Schrödinger cat state. This is what we did in our
experiments with cobalt niobate. We have tuned the system exactly in order
to turn it quantum critical."

By tuning the system and artificially introducing more quantum uncertainty
the researchers observed that the chain of atoms acts like a nanoscale
guitar string. Dr. Radu Coldea from Oxford University, who is the principal
author of the paper and drove the international project from its inception a
decade ago until the present, explains: "Here the tension comes from the
interaction between spins causing them to magnetically resonate. 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
, which is the golden ratio famous from art and
architecture." Radu Coldea is convinced that this is no coincidence. "It
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", he explains.

The observed resonant states in cobalt niobate are a dramatic laboratory
illustration of the way in which mathematical theories developed for
particle physics may find application in nanoscale science and ultimately in
future technology. Prof. Tennant remarks on the perfect harmony found in
quantum uncertainty instead of disorder. "Such discoveries are leading
physicists to speculate that the quantum, atomic scale world may have its
own underlying order. Similar surprises may await researchers in other
materials in the quantum critical state."

The researchers achieved these results by using a special probe - neutron
scattering. It allows physicists to see the actual atomic scale vibrations
of a system. Dr. Elisa Wheeler, who has worked at both Oxford University and
Berlin on the project, explains "using neutron scattering gives us
unrivalled insight into how different the quantum world can be from the
every day". However, "the conflicting difficulties of a highly complex
neutron experiment integrated with low temperature equipment and precision
high field apparatus make this a very challenging undertaking indeed." In
order to achieve success "in such challenging experiments under extreme
conditions" the HZB in Berlin has brought together world leaders in this
field. By combining the special expertise in Berlin whilst taking advantage
of the pulsed neutrons at ISIS, near Oxford, permitted a perfect combination
of measurements to be made.

More information: Quantum Criticality in an Ising Chain: Experimental
Evidence for Emergent E8 Symmetry. Article in Science,

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