Adiabatic effective action for vortices in neutral and charged superfluids at zero temperature are calculated using the topological Landau-Ginzburg theory recently proposed by Hatsuda, Yahikozawa, Ao and Thouless, and vortex dynamics are examined. The Berry phase term arising in the effective action naturally yields the Magnus force in both neutral and charged superfluids. It is shown that in neutral superfluid there is only one degree of freedom, namely the center of vorticities, and the vortex energy is proportional to the sum of all vorticities so that it is finite only for the vanishing total vorticity of the system. On the other hand the effective mass and the vortex energy for a vortex in charged superfluids are defined individually as expected. The effects of the vortex core on these quantities are also estimated. The possible depinning scenario which is governed by the Magnus force and the inertial mass is also discussed.
We derive an effective action for the vortex-position degree of freedom in a superfluid by integrating out condensate phase- and density-fluctuation environmental modes. When the quantum dynamics of environmental fluctuations is neglected, we confirm the occurrence of the vortex Magnus force and obtain an expression for the vortex mass. We find that this adiabatic approximation is valid only when the superfluid droplet radius
R, or the typical distance between vortices, is very much larger than the coherence length $\ensuremath{\xi}$. We go beyond the adiabatic approximation numerically, accounting for the quantum dynamics of environmental modes and capturing their dissipative coupling to condensate dynamics. For the case of an optical-lattice superfluid, we demonstrate that vortex motion damping can be adjusted by tuning the ratio between the tunneling energy
J and the on-site interaction energy
U. We comment on the possibility of realizing vortex-Landau-level physics.
We give a general review of recent developments in the theory of vortices in superfluids and superconductors, discussing why the dynamics of vortices is important, and why some key results are still controversial. We discuss work that we have done on the dynamics of quantized vortices in a superfluid. Despite the fact that this problem has been recognized as important for forty years, there is still a lot of controversy about the forces on and masses of quantized vortices. We think that one can get unambiguous answers by considering a broken symmetry state that consists of one vortex in an infinite ideal system. We argue for a Magnus force that is proportional to the superfluid density, and we find that the effective mass density of a vortex in a neutral superfluid is divergent at low frequencies. We have generalized some of the results for a neutral superfluid to a charged system.
A microscopic analysis of the nondissipative force
Fnd acting on a line vortex in a type-II superconductor at T=0 is given. All work presented assumes a charged BCS superconductor. We first examine the Berry phase induced in the BCS superconducting ground state by movement of the vortex and show how this phase enters into the hydrodynamic action
Shyd of the superconducting condensate. Appropriate variation of
Shyd give
Fnd and variation of the Berry phase term is seen to contribute the Magnus or lift force of classical hydrodynamics to
Fnd. This analysis, based on the BCS ground state of a charged superconductor, confirms in detail the arguments of Ao and Thouless within the context of the BCS model. Our Berry phase, in the limit e\ensuremath{\rightarrow}0, is seen to reproduce the Berry phase determined by these authors for a neutral superfluid. We also provide a second, independent, determination of
Fnd through a microscopic derivation of the continuity equation for the condensate linear momentum. This equation yields the acceleration equation for the superflow and shows that the vortex acts as a sink for the condensate linear momentum. The rate at which momentum is lost to the vortex determines
Fnd in this second approach and the result obtained agrees identically with the previous Berry phase calculation. The Magnus force contribution to
Fnd is seen in both calculations to be a consequence of the vortex topology and motion. A preliminary discussion is given regarding finite temperature extensions of the Berry phase calculation, with emphasis on its relevance for the sign anomaly occurring in Hall-effect experiments on type-II superconductors in the flux flow regime.
The transverse force on an isolated and moving vortex in a neutral superfluid at rest is evaluated at finite temperature in the case of noninteracting phonons. Using the Thouless, Ao, Niu (TAN) [Phys. Rev. Lett. 76, 3758 (1996)] general theory, we show that the transverse force is exactly equal to the superfluid Magnus force. We extend this theory in the case of a slowly moving vortex on a circular trajectory, and find an additional contribution coming from the centrifugal reaction. This term gives a negative vortex mass due to the phonons and diverges logarithmically at low frequency. The friction force is also evaluated for zero and finite frequencies, and compared with the scattering theory.
Starting from the time-dependent version of the Feynman-Hellmann theorem, the Magnus force acting on a vortex in fermion superfluid is expressed via the adiabatic curvature over the space of vortex positions. With use of the Bogoliubov--de Gennes approximation, the Magnus force in a homogeneous superfluid at T=0 is shown to originate from virtual transitions between the lowest quasiparticle core bound states. Nonadiabatic corrections to the curvature are obtained to second order in vortex velocity. The adiabatic approximation is shown to break down at a critical velocity equal to the vortex velocity in the first Landau level. The effect of elastic scattering on the Magnus force is discussed in terms of the relaxation-time approximation. It is suggested that this approximation is appropriate only for a large-scale vortex motion. In this case, the effective Magnus force is drastically reduced when the elastic-scattering rate exceeds the core excitation frequency. We conjecture that quantum vortex tunneling is governed by a local Magnus force obtained from the Berry phase approach.
We derive an effective action for the vortex-position degree of freedom in a superfluid by integrating out condensate phase- and density-fluctuation environmental modes. When the quantum dynamics of environmental fluctuations is neglected, we confirm the occurrence of the vortex Magnus force and obtain an expression for the vortex mass. We find that this adiabatic approximation is valid only when the superfluid droplet radius R ,o r the typical distance between vortices, is very much larger than the coherence length ξ. We go beyond the adiabatic approximation numerically, accounting for the quantum dynamics of environmental modes and capturing their dissipative coupling to condensate dynamics. For the case of an optical-lattice superfluid, we demonstrate that vortex motion damping can be adjusted by tuning the ratio between the tunneling energy J and the on-site interaction energy U. We comment on the possibility of realizing vortex-Landau-level physics.