Magnus and Iordanskii Forces in Superfluids

Abstract

The total transverse force acting on a quantized vortex in a superfluid is a problem that has eluded a complete understanding for more than three decades. In this letter I propose a remarkably simple argument, somewhat reminiscent of Laughlin's beautiful argument for the quantization of conductance in the quantum Hall effect, to define the superfluid velocity part of the transverse force. This term is found to be $-{\rho }_s{\kappa }_s\times v_s$. Although this result does not seem to be overly controversial, this thermodynamic argument based only on macroscopic properties of the superfluid does offer a robust derivation. A recent publication by Thouless, Ao and Niu has demonstrated that the vortex velocity part of the transverse force in a homogeneous neutral superfluid is given by the usual form ${\rho }_s{\kappa }_s\times v_V$. A combination of these two independent results and the required Galilean invariance yields that there cannot be any transverse force proportional to the normal fluid velocity, in apparent conflict with Iordanskii's theory of the transverse force due to phonon scattering by the vortex.

RevTex, 1 Encapsulated Postscript figure

References in corpus (1)

• The Magnus force in superfluids and superconductors

Cited by in corpus (24)

• Dynamic vortex mass in clean Fermi superfluids and superconductors
• Acoustic Energy and Momentum in a Moving Medium
• Extending Luttinger's theorem to Z(2) fractionalized phases of matter
• Iordanskii Force and the Gravitational Aharonov-Bohm effect for a Moving Vortex
• Magnetic Force Exerted by the Aharonov-Bohm Line (II)
• Vortices in holographic superfluids and superconductors as conformal defects
• Energy cascade with small-scales thermalization, counterflow metastability and anomalous velocity of vortex rings in Fourier-truncated Gross-Pitaevskii equation
• Vortex vs spinning string: Iordanskii force and gravitational Aharonov-Bohm effect
• Luttinger's theorem, superfluid vortices, and holography
• Incompatibility of long-period neutron star precession with creeping neutron vortices
• Microscopic theory of vortex dynamics in homogeneous superconductors
• Sound-induced vortex interactions in a zero-temperature two-dimensional superfluid
• Vortex Formation and Dynamics in Superfluid 3He and Analogies in Quantum Field Theory
• Motion of a superfluid vortex according to holographic quantum dissipation
• Transverse force on a quantized vortex in a superconductor
• Vortex Dynamics in the Two-Fluid Model
• Scattering of Phonons by a Vortex in a Superfluid
• Mutual friction in superfluid ${}^3$He-B in the low-temperature regime
• Superfluid dynamics in neutron star crusts: the Iordanskii force and chemical gauge covariance
• Global singularity-free solution of the Iordanskii force problem
• Quantum vortices in fermionic superfluids: from ultracold atoms to neutron stars
• Time-Dependent Density-Functional Theory for Superfluids
• Generalization of the Kutta-Joukowski theorem for the hydrodynamic forces acting on a quantized vortex
• Quantum vortex dipole as a probe of the normal component distribution