The Superfluid Phases Of Helium 3

Vollhardt, D.; Wölfle, P.; Hallock, R. B.

doi:10.1201/b12808

Cited by 1,124 publications

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“…The initial state is a non-dissipative vortex sheet -the interface between two superfluids brought into a state of relative shear flow. So far the only experimentally accessible case where this can be studied in stationary conditions, is the interface between 3 He-A and 3 He-B [8], where the order parameter changes symmetry and magnitude, but is continuous on the scale of the superfluid coherence length ξ ∼ 10 nm. We discuss an experiment, where the two phases slide with respect to each other in a rotating cryostat:…”

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Shear Flow and Kelvin-Helmholtz Instability in Superfluids

Blaauwgeers¹,

et al. 2002

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The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3 He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with a modified Kelvin-Helmholtz theory.Instabilities in the shear flow between two layers of fluids [1] belong to a class of interfacial hydrodynamics which is attributed to many natural phenomena. Examples are wave generation by wind blowing over water [2], the flapping of a sail or flag in the wind [3,4], and even flow in granular beds [5]. In the hydrodynamics of inviscid and incompressible fluids the transition from calm to wavy interfaces is known as the Kelvin-Helmholtz (KH) instability [6,2]. Since Lord Kelvin's treatise in 1871, difficulties have plagued its description in ordinary fluids, which are viscous and dissipative. They also display a shear-flow instability, but its correspondence with that in the ideal limit is not straightforward. The tangential velocity discontinuity in the shear-flow instability is created by a vortex sheet. In a viscous fluid a planar vortex sheet is not a stable equilibrium state and not a solution of the hydrodynamic equations [7].Superfluids provide a close variation of the ideal inviscid limit considered by Lord Kelvin and thus an environment where the KH theory can be tested. The initial state is a non-dissipative vortex sheet -the interface between two superfluids brought into a state of relative shear flow. So far the only experimentally accessible case where this can be studied in stationary conditions, is the interface between 3 He-A and 3 He-B [8], where the order parameter changes symmetry and magnitude, but is continuous on the scale of the superfluid coherence length ξ ∼ 10 nm. We discuss an experiment, where the two phases slide with respect to each other in a rotating cryostat:3 He-A performs solid-body-like rotation while 3 He-B is in the vortex-free state and thus stationary in the laboratory frame. While increasing the rotation velocity Ω, we record the events when the AB phase boundary becomes unstable -when some circulation from the A-phase crosses the AB interface and vortex lines are introduced into the initially vortex-free B phase. On increasing the rotation further, the instability occurs repeatedly. Such a succession of instability events can be understood as a spin-up of 3 He-B by rotating 3 He-A. Our experimental setup is shown in Fig. 1. The AB boundary is forced against a magnetic barrier in a smooth-walled quartz container, by cooling the sample below T AB at constant pressure in a rotating refrigerator. The number of vortices in both phases is indepe...

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“…No fitting parameters are used. The values for σ(T ), χA − χB(T, H), and ρs(T ) are obtained from accepted references [8,[18][19][20], while H and ∇H apply for the profile H(z) at the location of the AB boundary:…”

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Shear Flow and Kelvin-Helmholtz Instability in Superfluids

Blaauwgeers¹,

et al. 2002

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“…The threshold energy 2ν in the molecular kinetic energy ε B q + 2ν ≡ q/2M + 2ν is independent of j, due to the spherical symmetry of the system we are considering. In the last term, g r is the coupling constant of a p-wave Feshbach resonance, with p j characterizing the p-wave symmetry [18].…”

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BCS-BEC Crossover in a Gas of Fermi Atoms with ap-Wave Feshbach Resonance

Ōhashi

2005

Phys. Rev. Lett.

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We investigate unconventional superfluidity in a gas of Fermi atoms with an anisotropic p-wave Feshbach resonance. Including the p-wave Feshbach resonance as well as the associated three kinds of quasi-molecules with finite orbital angular momenta L z = ±1, 0, we calculate the transition temperature of the superfluid phase. As one passes through the p-wave Feshbach resonance, we find the usual BCS-BEC crossover phenomenon. The p-wave BCS state continuously changes into the BEC of bound molecules with L = 1. Our calculation includes the effect of fluctuations associated with Cooper-pairs and molecules which are not Bose-condensed.

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“…[23,24]), where Ginzburg-Landau (GL) free energy terms, describing the FS phase were derived by symmetry group arguments. The non-unitary state, with a non-zero value of the Cooper pair magnetic moment, known from the theory of unconventional superconductors and superfluidity in 3 He [1], has been suggested firstly in Ref. [23], and later confirmed in other studies [7,24]; recently, the same topic was comprehensively discussed in Ref.…”

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Theory of Ferromagnetic Unconventional Superconductors with Spin-Triplet Electron Pairing

Uzunov¹

2012

Superconductors - Materials, Properties and Applications

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The Superfluid Phases Of Helium 3

Cited by 1,124 publications

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Shear Flow and Kelvin-Helmholtz Instability in Superfluids

Shear Flow and Kelvin-Helmholtz Instability in Superfluids

BCS-BEC Crossover in a Gas of Fermi Atoms with ap-Wave Feshbach Resonance

Theory of Ferromagnetic Unconventional Superconductors with Spin-Triplet Electron Pairing

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