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model describes avalanche behavior of superfluid helium
James E. Kloeppel,
Physical Sciences Editor
photo to enlarge
by L. Brian Stauffer
professor Paul Goldbart, right,
with postdoctoral research associate Roman Barankov,
left, and graduate student David Pekker have
constructed a model that describes the avalanche-like,
phase-slip cascades in the superflow of helium.
CHAMPAIGN, Ill. —
By utilizing ideas developed in disparate fields, from earthquake dynamics
to random-field magnets, researchers at the University of Illinois have
constructed a model that describes the avalanche-like, phase-slip cascades
in the superflow of helium.
Just as superconductors have no electrical resistance, superfluids have
no viscosity, and can flow freely. Like superconductors, which can be
used to measure extremely tiny magnetic fields, superfluids could create
a new class of ultra-sensitive rotation sensors for use in precision
guidance systems and other applications.
But, before new sensors can be built, scientists and engineers must
first acquire a better understanding of the odd quirks of superfluids
arising in these devices.
In the April 23 issue of Physical Review Letters, U. of I. physicist
Paul Goldbart, graduate student David Pekker and postdoctoral research
associate Roman Barankov describe a model they developed to explain
some of those quirks, which were found in recent experiments conducted
by researchers at the University of California at Berkeley.
In the Berkeley experiments, physicist Richard Packard and his students
Yuki Sato and Emile Hoskinson explored the behavior of superfluid helium
when forced to flow from one reservoir to another through an array of
several thousand nano-apertures. Their intent was to amplify the feeble
whistling sound of phase-slips associated with superfluid helium passing
through a single nano-aperture by collecting the sound produced by all
of the apertures acting in concert.
At low temperatures, this amplification turned out, however, to be surprisingly
weak, because of an unanticipated loss of synchronicity among the apertures.
“Our model reproduces the key physical features of the Berkeley
group’s experiments, including a high-temperature synchronous
regime, a low-temperature asynchronous regime, and a transition between
the two,” said Goldbart, who also is a researcher at the university’s Frederick Seitz Materials Research
The theoretical model developed by Pekker, Barankov and Goldbart balances
a competition between interaction and disorder – two behaviors
more commonly associated with magnetic materials and sliding tectonic
The main components of the researchers’ model are nano-apertures
possessing different temperature-dependent critical flow velocities
(the disorder), and inter-aperture coupling mediated by superflow in
the reservoirs (the interactions).
For helium, the superfluid state begins at a temperature of 2.18 kelvins.
Very close to that temperature, inter-pore coupling tends to cause neighbors
of a nano-aperture that already has phase-slipped also to slip. This
process may cascade, creating an avalanche of synchronously slipping
phases that produces a loud whistle.
However, at roughly one-tenth of a kelvin colder, the differences between
the nano-apertures dominate, and the phase-slips in the nano-apertures
are asynchronous, yielding a non-avalanching regime. The loss of synchronized
behavior weakens the whistle.
“In our model, competition between disorder in critical flow velocities
and effective inter-aperture coupling leads to the emergence of rich
collective dynamics, including a transition between avalanching and
non-avalanching regimes of phase-slips,” Goldbart said. “A
key parameter is temperature. Small changes in temperature can lead
to large changes in the number of phase-slipping nano-apertures involved
in an avalanche.”
The work was funded by the U.S. Department of Energy and the National
Editor’s note: To reach Paul Goldbart,
call 217-333-1195; e-mail: email@example.com.