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Pg 14, column 2, equation 1: [ρs ∝(Tλ −T)2/3]
Pg 14, column 2, equation 2:
Because is a Galilean invariant, it is a legitimate
the persistent current and make a quantitative determina- tion of its decay rate, not a trivial task because the flow only decays by about 10% over the age of the universe! He was able to excite fourth sound in a cylindrical resonator and later in a toroidal resonator, into which a persistent current was introduced by rotating that resonator at a temperature above Tλ and then reducing the temperature below Tλ and letting the resonator come to rest.
The flowing superfluid split the degeneracy of the waves that propagate clockwise and counterclockwise, allowing those split modes to beat against each other. (Izzy always said, “Know your modes.”) The beat frequency gave a pre- cise measure of the superflow velocity, with the first mea- surement occurring less than a second after the rotation stopped. That prompt result was critical because the decay of the supercurrent is logarithmic in time (like flux unpin- ning in Type II superconductors); measuring two decades of decay in the first minute contains as much information as you would obtain in 100 hours if you had to wait an hour to make your first measurement.
Third and Fifth Sounds
One of Izzy’s favorite modes was third sound, a surface wave that can be excited on atomically thin adsorbed films of su- perfluid helium (Putterman and Garrett, 1999). As shown in Figure 2c, the normal-fluid component is again immobi- lized by its viscosity. He liked third sound partly because it dramatically demonstrated one his favorite maxims,
“Superfluid helium obeys the laws of quantum mechanics on the macroscopic level and the laws of hydrodynamics on the microscopic level.”
In films that were 1-2 atomic layers thick, he observed propa- gating modes by measuring the small change in temperature that they induced. This was accomplished with evaporated metal films operating near their superconducting transition.
In 1969, about three years before the Nobel Prize-winning Kosterlitz-Thouless theory of two-dimensional phase transi- tions was formulated, Izzy emphasized the universal aspects of the disappearance, as the film thickness decreased, of third sound at nonzero propagation velocities: “Superfluid- ity is disappearing at a finite speed of third sound so some- thing deep must be going on.” Apparently, the Nobel Prize Committee agreed. These third sound measurements, made with Ken Telschow, Taylor Wang, E. O. McLean, and John Scholtz, still comprise the most accurate test of the Koster- litz-Thouless theory.
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t*he∂rρm/∂odvyn−avmic va-riable, although its influence can only
+ %$ ( n s ) (' T , P .
manifest in the regime of nonlinear acoustics.
Fourth Sound
It is also possible to immobilize the normal-fluid component
when superfluid helium permeates a porous medium, like a tirghtlry p2acked powder. That case is illustrated schematically
Pg 14, column 2, equation 3:
(v −v ) ns
in Figure 2d. Izzy’s group was the first to observe this fourth
sound mode, which is restored by the fluid’s compressibility,
and was the first to measure its velocity as a function of tem-
Pg 15, column 1:
perature, which necessarily vanishes above the λ-transition [c2 =(ρ /ρ)c2].
4s1
Because fourth sound propagates in tiny pores, it was pos- sible for Étienne Guyon, Mike Kriss, Ray Scott, and Ken Sha- piro to use fourth sound to determine the reduction in ρs /ρ and Tλ due to the healing length effects produced by the sup- pression of the quantum mechanical wave function in con- fined geometries. What is less obvious is that simultaneous measurement of the speeds c1, c2, and c4 is sufficient to pro- duce an accurate determination of all the thermodynamic properties of He II if the fluid’s density is known at a single point! Joe Heiserman, Jean-Pierre Hulin, and Jay Maynard simultaneously measured c1, c2, and c4 at more than 400 points over the pressure-temperature plane, making it pos- sible for Maynard to determine the density, thermal expan- sion coefficient, normal-fluid fraction, specific entropy and specific heat at a constant pressure, the polytropic coefficient (i.e., ratio of specific heats), and isothermal compressibility. With the relative uncertainty of the sound speed measure- ments below ±0.2%, the resulting thermodynamic tables are still the best available.
Subsequent observation of the fourth sound mode by one of Izzy’s former students, Haruo Kojima, was proof of superfluid- ity in the rare isotope 3He and demonstrated that this new su- perfluid also behaves in accordance with the two-fluid theory.
Persistent Currents
One of the most astonishing features of superconductivity is the ability to produce an electrical current in a supercon- ducting ring that will persist indefinitely. Such electrical currents are easy to observe due to the magnetic field such persistent currents produce. Because superfluids flow with- out viscosity, it should also be possible to create superfluid persistent currents. Because He II is an electrically neutral fluid, there would be no telltale magnetic signature for flow.
With Haruo Kojima, Wolfgang Veith, Seth Putterman, and Etienne Guyon, Izzy exploited fourth sound to determine
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