H. E. Hall

Momentum creation by vortices in superfluid 3He as a model of primordial baryogenesis

The Universe contains much more matter than antimatter, which is probably the result of processes in the early Universe in which baryon number was not conserved. These processes may have occurred during the electroweak phase transition, when elementary particles first acquired mass1–4. It is impossible to study directly processes relevant to the early Universe, because of the extreme energies involved. One is therefore forced to investigate laboratory systems with analogous phase transitions. Much of the behaviour of superfluid 3He is analogous to that predicted within the standard model of the electroweak interaction5. Superfluids and liquid crystals have already been used to investigate cosmic string production6–11; here we describe experiments on 3He that demonstrate the creation of excitation momentum (which we call momentogenesis) by quantized vortices in the superfluid. The underlying physics of this process is similar to that associated with the creation of baryons within cosmic strings, and our results provide quantitative support for this type of baryogenesis.

Vibrating wire measurements in liquid3He. I. The normal state

A vibrating wire viscometer has been constructed using superconducting wire of diameter 58 µm in the form of a semicircular loop of radius 1.4 cm fixed at both ends and oscillating in a direction perpendicular to the plane of the loop. The use of the viscometer to measure the viscosity of normal phase3He is described and the corrections that have been applied to the data to allow for the finiteQ of the resonance, a quasiparticle mean free path comparable to the wire diameter, and a viscous penetration depth comparable to the size of the channel containing the wire are discussed. The measured viscosities show small departures from the ηT2=const law of Fermi liquid theory similar to those observed in some but not all previous measurements. The values of the viscosity at the superfluid transition temperature agree with those obtained in other measurements.

Errata: Vibrating wire measurements in liquid3He. II. The superfluid B phase

Measurements with a vibrating wire viscometer in superfluid3He-B at temperatures down to 0.6 mK are described. The need to consider compressibility of the superfluid component in any analysis of vibrating wire measurements is clearly demonstrated and a theoretical calculation of the force acting on a vibrating wire in a finite compressible superfluid is given. The experimental data are consistent with this calculation if theoretical values of the second viscosity ξ3 are used in the analysis. The failure of the hydrodynamic theory when the quasiparticle mean free path1 is comparable to the wire radius a was observed, and an expression has been deduced for the force acting on the wire when1 is finite. Experimental and theoretical evidence is presented to show that this expression is valid for arbitrary1/a. Values of the viscosity obtained using this expression agree with those obtained in other experimental work and confirm the large discrepancy with theoretical calculations at low reduced temperatures.

Vortex mutual friction in rotating superfluid3He

The Manchester rotating cryostat has been used to measure the longitudinal and transverse coefficients of vortex mutual friction in the A and B phases of superfluid3He. In the B phase the dominant contribution to the mutual friction is scattering of excitations off occupied bound states in the vortex core. The A phase results are explained quantitatively by assuming that doubly quantised continuous vortices are created with a dynamics determined by the equation of motion of the orbital vectorI; the measurements enable us to put an upper limit on the orbital inertia of less than 0.01h per Cooper pair. History-dependent textural effects which had to be overcome in order to make meaningful measurements in the A phase are explained by noting that for a given rotation direction the most stable vortices can be formed more easily from one direction of uniformI texture than the other.

Diaphragm-driven flow in rotating superfluid 3He-B

We present the theory used to analyse experiments at Manchester University in which we observe the normal modes of transverse vibration of a Kapton diaphragm separating two nominally identical disc-shaped regions of superfluid 3He, each of height 100 μm and diameter 40 mm. From the mode frequencies we deduce information on the superfluid density and hence on strong coupling corrections to the energy gap. From the dissipation the first and second viscosities, η and ξ3, of the fluid can be obtained. Rotation of the experiment about an axis perpendicular to the diaphragm creates a lattice of quantised vortex lines. We show how the mutual friction parameters B and B′ can be determined from the effect of the vortices on the normal modes of the diaphragm.

Metastability and hysteresis of the vortex states in rotating superfluid3He-B

We have investigated the vortex core transition in3He-B by measuring the associated changes in mutual fricition dissipation within the superfluid. If rotation is continuously stopped and restarted while cooling or warming then the transition occurs at a clearly defined temperature, but temperature sweeps during continuous rotation show substantial supercooling and superheating. Moreover, the high temperature vortex shows a continuum of metastable states when supercooled to a constant, arbitrary low temperature, the mutual friction dissipaton depending on the temperature at which rotation was started. Our current interpretation is that the high temperature vortex state is a temperature-dependent mixture of two vortex types.

Rotating millikelvin cryostat

Abstract We describe the construction and operation of a rotatable nuclear refrigeration cryostat. Special features include air bearings at the level of the cryostat cap designed for ease of maintenance, a drive linkage that transmits a pure torque to the cryostat, and large diameter rotating vacuum seals to enable the dilution refrigerator to be operated by a standard booster pump.

History-dependent nonlinear dissipation in superfluid3He-A

AbstractWe have studied nonlinear dissipation in oscillatory flow of3He-A through 49-µm- and 17-µm-wide channels by means of torsion pendulum experiments at about 50 Hz. The observed effects are strongly history dependent; the dissipation at a given measuring amplitude is strongly increased if the sample is cooled through Tc while oscillating at large amplitude. Once a highly dissipative state has been created it does not noticeably decay below Tc, though a more dissipative state can be created below Tc by a period of sufficiently large-amplitude oscillation. The results are described semiquantitatively by a model based on the idea of superflow collapse by motion of the

NMR investigation of the magnetic susceptibility anisotropy in3He-A

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