Third-Sound Velocity and Onset on Grafoil

Abstract

is sometimes overlooked, when insufficient care is taken in specifying the variable that is to be identified with the chemical potential. This point is discussed in Ref. 4. In addition, because of the vector character of the 3 He-A order parameter, there is an explicit term proportional to f° V x v" in the equation governing the time rate of change of the effective phase. This additional term is strongly emphasized in Ref. 1, but the first term is also implicit in their discussion and can produce fully comparable effects. 8 We emphasize that this circulation (which is the hydrodynamical manifestation of the crucial nonuniformity in the initial order parameter) is essential for the appearance of the gauge-wheel effect. The circulation distinguishes this geometry from ordinary superfluid couette-flow experiments, which are not necessarily carried out against a fixed background supercurrent. 9 The same effect will take place in the A phase of superfluid helium-3 in the presence of a circulating supercurrent, even when the anisotropy axis is radial. 10 In a nonlinear analysis the heat current at the opposite wall is determined by the bulk entropy production. In a linear analysis the entropy production is second order and the thermal current can be taken to vanish for all x.u We use these in the form given by I. M. Khalatnikov, An Introduction to the Theory of Superfluidity (Benjamin, New York, 1965), p. 66.We use the symbol /Lt s to denote what Khalatnikov denotes by the symbol pi. Since whatever name one gives it, the quantity is determined by the hydrodynamics, this change in nomenclature has no consequence for our analysis. However we shall show in Ref. 4 that what is conventionally called the chemical potential in many treatments of superfluid hydrodynamics is, in fact, the chemical potential in the local rest frame of the superfluid ix a . This differs from the true chemical potential IJL by terms of second order in v n and v s O-i 3^ +iv s 2 -v" ° v 5 ) and for many purposes j* and p s can be identified. In the case of gauge-wheel effects the secondorder terms are of crucial importance, and one loses considerable insight into the underlying physics by confusing pt 5 with \k. In particular, the fact that the twofluid hydrodynamics gives a constant \k s is not incompatible with our earlier assertion that the phase winding is balanced by a (true) chemical-potential gradient in the steady state. 13 This does not necessarily imply that the temperature drop remains unmeasurably small as w increases, though when w/v » 1, the fluid may respond through vortex nucleation rather than by producing a chemical potential (and hence temperature) drop. Note that from this point of view gauge-wheel effects are cleaner in 4 He than in 3 He-A, since the possibility for similar complications due to textural motions is absent in the more common superfluid.

Liquid and solid 4He near a graphite wall

“…At zero external pressure, the van der Waals attraction is sufficient to nucleate one-two atomic layers of solid on all common substrates. Graphite turns out to be different in the sense that although the solid 4He on its surface should have a thickness similar to that on other materials, experimental evidence shows that 4He becomes superfluid only after four atomic layers are deposited (6,7). This implies a solid thickness of three layers, twice the amount expected.…”

Buffer gas cooling and trapping of atoms with small effective magnetic moments

“…We model this desorption using simple gas dynamics: the 3 He desorption rate [13] ṅd = P (d)fA/V 2πk B T cell (t)m, where m is the 3 He mass, f is the sticking fraction (taken to be 0.75) [20], A = 420 cm 2 is the surface area of the cell, and the vapor pressure P is related to the film thickness d and the saturated vapor pressure P 0 by the FHH expression [21] P = P 0 exp[−α/T cell (t)d 3 ]. We assume the van der Waals coefficient [22] α = 1900 K Å3 and use the measured T cell (t) shown in the inset of fig.…”