Mutual friction force in rotating helium II at low temperatures and near the ?-point

Sonin, É. B.

doi:10.1007/bf00117424

Cited by 14 publications

(10 citation statements)

References 12 publications

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“…(10.12), so his theory agrees with that of Pitaevskii (1977) and Sonin (1981b). ' The numerical estimate by Onuki, 1975).…”

Section: Vortex Oscillatigns and Hydrodynamics Of A Rotating Anissupporting

confidence: 69%

“…Hence it is expected that vortex pinning strongly affects the counterflow. This is discussed in more detail by Sonin (1981b). The theory of mutual friction near the k point has also been developed by Onuki (1983a).…”

Section: Vortex Oscillatigns and Hydrodynamics Of A Rotating Anismentioning

confidence: 93%

“…The methods used by Sonin (1981b) andOnuki (1983a) to obtain the equation of motion for vortices are also similar. They are based on the absence of secular terms in the equations describing the superfluid around the moving vortex.…”

Section: Vortex Oscillatigns and Hydrodynamics Of A Rotating Anismentioning

confidence: 97%

“…The resultant theory, called the phenomenological 4' theory, was considered in the reviews of Sobyanin (1976, 1982). Within the scope of this theory the coefficients 8 and 8' in the critical region have been calculated (Sonin, 1981b). Results of these calculations are better presented in the parameters g and g' connected with B and B' by the complex expression given by the coefficient g3 -flA/2Mp Thus the second term in g may be interpreted as the contribution of the second viscosity to the mutual friction, proportional to the coefficient g3.…”

Section: Vortex Oscillatigns and Hydrodynamics Of A Rotating Anismentioning

confidence: 99%

“…He used the phenomenological theory, which is a generalization of Hohenberg and Halperin's (1977) model F. This theory is equivalent to the 0' theory except that Onuki assumed the relaxation parameter A to be complex. In addition, Onuki took into account corrections due to the thermal conductivity, which had been ignored by Sonin (1981b).…”

Section: Vortex Oscillatigns and Hydrodynamics Of A Rotating Anismentioning

confidence: 99%

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Vortex oscillations and hydrodynamics of rotating superfluids

Sonin

1987

Rev. Mod. Phys.

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361

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This review covers the progress in the study of vortex oscillations in rotating superfluids. The paper deals with the theory as its principal coricern, but the experimerits that one can compare with the theory considered are also discussed. Attention is focused mainly on the d'fects of crystalline order in the vorte~lattice (the Tkachenko waves especially) and on the boundary problems arising in studies of vortex oscillations in finite containers. The approach is based mostly on the continuum hydrodynamic theory dealing with dense vortex arrays, and considerable attention is devoted to discussion of this theory in order to understand better the principles upon which the obtained results rest. The theory is traced from the simple description of a rotating classical fluid with continuous vorticity, through that of a perfect fluid with quantized vorticity in the form of an array of vortex lines, then the two-fluid theory of an isotropic superfluid, and finally the theory of rotating anisotropic superfluids such as He-A. Applications of the theory to He II, the superfluid phases of He, and the superfluid neutron matter in pulsars are discussed. CONTENTS

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“…(10.12), so his theory agrees with that of Pitaevskii (1977) and Sonin (1981b). ' The numerical estimate by Onuki, 1975).…”

Section: Vortex Oscillatigns and Hydrodynamics Of A Rotating Anissupporting

confidence: 69%

Section: Vortex Oscillatigns and Hydrodynamics Of A Rotating Anismentioning

confidence: 93%

Section: Vortex Oscillatigns and Hydrodynamics Of A Rotating Anismentioning

confidence: 97%

Section: Vortex Oscillatigns and Hydrodynamics Of A Rotating Anismentioning

confidence: 99%

Section: Vortex Oscillatigns and Hydrodynamics Of A Rotating Anismentioning

confidence: 99%

See 3 more Smart Citations

Vortex oscillations and hydrodynamics of rotating superfluids

Sonin

1987

Rev. Mod. Phys.

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361

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Magnus Force and Aharonov—Bohm Effect in Superfluids

Sonin¹

2002

Springer Series in Solid-State Sciences

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The paper addresses the problem of the transverse force (Magnus force) on a vortex in a Galilean invariant quantum Bose liquid. Interaction of quasiparticles (phonons) with a vortex produces an additional transverse force (Iordanskii force). The Iordanskii force is related to the acoustic Aharonov-Bohm effect. Connection of the effective Magnus force with the Berry phase is also discussed.The key role of the Magnus force in vortex dynamics became clear from the very beginning of studying superfluid hydrodynamics. In the pioneer article on the subject Hall and Vinen [2] defined the superfluid Magnus force as a force between a vortex and a superfluid. Therefore it was proportional to the superfluid density ρ s . But in the two-fluid hydrodynamics the superfluid Magnus force is not the only force on the vortex transverse to its velocity: there was also a transverse force between the vortex and quasiparticles moving with respect to the vortex. The transverse force from rotons was found by Lifshitz and Pitaevskii [3] from the quasiclassical scattering theory. Later Iordanskii [4] revealed the transverse force from phonons. The analysis done in Ref.[5] (see also Refs. [6,7]) demonstrated that the Lifshitz-Pitaevskii force for rotons and the Iordanskii force for phonons originate from interference between quasiparticles which move past the vortex on the left and on the right sides with different phase shifts, like in the Aharonov-Bohm effect [8]. Since the phase shift depends on the circulation which is a topological charge for a vortex, this is a clear indication of connection between the transverse quasiparticle force and topology.Later on the analogy between wave scattering by vortex and electron scattering by the magnetic-flux tube (the Aharonov-Bohm effect) was studied in classical hydrodynamics for water surface waves (the acoustic Aharonov-Bohm effect [9,10]). Scattering of the light by a vortex also results in the Aharonov-Bohm interference (the optical Aharonov-Bohm effect [11]). As follows from Ref.[5], the Aharonov-Bohm interference always produces a transverse force on the vortex, or the fluxon. For the original Aharonov-Bohm effect this force is discussed by Shelankov [12].The Magnus force on a vortex in a superconductor was introduced by Nozières and Vinen [13]. The total transverse force on a vortex is responsible for the Hall effect in the mixed state. In superconductors not only quasiparticles, but also impurities produce an additional transverse force on the vortex. A reader can find discussion of this problem in the review by Kopnin [14].Despite a lot of work done to understand and calculate the Magnus force, it remained to be a controversial issue. Ao and Thouless [15] pointed out a connection of the Magnus force with the Berry phase [16] which is the phase variation of the quantum-mechanical wave function resulting from transport of the vortex round a close loop. From the Berry-phase analysis Ao and Thouless concluded that the effective Magnus force is proportional to the

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On the theory of superfluidity of helium II near the ? point

Ginzburg

Sobyanin

1982

J Low Temp Phys

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Mutual friction force in rotating helium II at low temperatures and near the ?-point

Cited by 14 publications

References 12 publications

Vortex oscillations and hydrodynamics of rotating superfluids

Vortex oscillations and hydrodynamics of rotating superfluids

Magnus Force and Aharonov—Bohm Effect in Superfluids

On the theory of superfluidity of helium II near the ? point

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