Due to strong interactions between superfluid particles, many particles are not in the condensate near absolute zero. In nonequilibrium situations produced under external stirring, they contribute to the flow via their induced average macroscopic motion. We present a modification of the Bose condensate model that considers this induced internal motion. Specifically, we show that the velocity field of the internal motion acts as a gauge field with which the condensate interacts, thereby coupling the applied vorticity to the superflow. The resulting Ginzburg-Landau-like model predicts the flow phenomena observed near absolute zero, in particular, transition to turbulence.
Due to strong interactions between superfluid particles, many particles are not in the condensate near absolute zero. In nonequilibrium situations produced under external stirring, they contribute to the flow via their induced average macroscopic motion. We present a modification of the Bose condensate model that considers this induced internal motion. Specifically, we show that the velocity field of the internal motion acts as a gauge field with which the condensate interacts, thereby coupling the applied vorticity to the superflow. The resulting Ginzburg-Landau-like model predicts the flow phenomena observed near absolute zero, in particular, transition to turbulence.
Abstract We present a gauge-field extension of the Bose condensate model that describes T ≈ 0 superfluid turbulence generated by the macroscopic motion of the superfluid. We first establish that the condensate model is dual to the short-range interacting loop gas model, wherein the loops represent quantum vortex lines. Vortex lines form, interact and proliferate as a result of the superfluid motion. Our extension is based on incorporating the Biot–Savart interaction between vortex lines, which is lacking in the loop gas model. We show that the extended loop gas is dual to a Ginzburg–Landau model, wherein the gauge coupling is between the macroscopic velocity field of the superfluid and the condensate. Applying the model to cylindrical and pipe flows, we describe how turbulence transitions with and without intermediate vortex flow, respectively.
In this work, we study the linear stability of superfluid phases of matter irrespective of the nature of microscopic degrees of freedom and the strength of interactions between them. Famously, assuming invariance under Galilean boosts and a phonon-roton single-particle dispersion relation, Landau predicted superfluid helium 4 would become unstable for large enough superfluid velocities. Here, we demonstrate that such instabilities generically follow from a change of sign of one of the eigenvalues of the matrix of second derivatives of the free energy. Our only assumption is the existence of static thermodynamic equilibrium, irrespective of any invariance under boosts or microscopic statistics. Turning on dissipation, we show that a linear dynamical instability also develops, leading to exponential growth in time of perturbations around equilibrium. Specializing to Galilean superfluids and assuming the existence of bosonic quasiparticles, our criterion reproduces Landau's critical velocity for Bose-Einstein condensates. Our criterion also reduces to the well-known maximal supercurrent in weakly coupled superconductors described either by Landau-Ginzburg or Bardeen-Cooper-Schrieffer theory. Further, it correctly reproduces the onset of the instability in relativistic, strongly coupled superfluids without quasiparticles at zero as well as finite temperature, which we construct using gauge/gravity duality. As a less trivial application of our criterion, we show that in dirty superfluids the instability manifests itself first in the thermal diffusion mode instead of the superfluid sound mode. Our work provides a simple, comprehensive, and unified description of the large superflow instability of superfluids and superconductors at any temperature independent of the microscopic details of the system and the strength of interactions.
Fluid turbulence remains an open problem in contemporary physics. In gases or liquids encountered in daily life, turbulence is comprised of swirling vortices of varying sizes, shapes and strengths. The impossibility of making detailed predictions of turbulent flows comes, in part, from the complicated nature of these vortices. Turbulence in quantum mechanical superfluids, on the other hand, is comparatively simple. When stirred, a superfluid produces well-defined, discretised vortex lines, and hence turbulence in these fluids is much more straightforward to interpret. As such, there is hope that the study of vortices in superfluids may hold the key to unlocking the mysteries of turbulence.
We carry out extensive direct numerical simulations to investigate the interaction of active particles and fields in the two-dimensional Gross-Pitaevskii superfluid, in both simple and turbulent flows. The particles are active in the sense that they affect the superfluid even as they are affected by it. We tune the mass of the particles, which is an important control parameter. At the one-particle level, we show how light, neutral, and heavy particles move in the superfluid, when a constant external force acts on them; in particular, beyond a critical velocity, at which a vortex-antivortex pair is emitted, particle motion can be periodic or chaotic. We demonstrate that the interaction of a particle with vortices leads to dynamics that depends sensitively on the particle characteristics. We also demonstrate that assemblies of particles and vortices can have rich, and often turbulent, spatiotemporal evolution. In particular, we consider the dynamics of the following illustrative initial configurations: (a) one particle placed in front of a translating vortex-antivortex pair; (b) two particles placed in front of a translating vortex-antivortex pair; (c) a single particle moving in the presence of counter-rotating vortex clusters; (d) four particles in the presence of counter-rotating vortex clusters. We compare our work with earlier studies and examine its implications for recent experimental studies in superfluid helium and Bose-Einstein condensates.
A possibility of the condensation of excitations with non-zero momentum in moving superfluid media is considered in terms of the Ginzburg-Landau model. The results might be applicable to the superfluid 4He, ultracold atomic Bose gases, various superconducting and neutral systems with pairing, like ultracold atomic Fermi gases and the neutron component in compact stars. The order parameters, the energy gain, and critical velocities are found.
This thesis examines the manifestation of the critical velocity for superfluidity in dilute gas Bose-Einstein condensates (BECs). Superfluidity is a macroscopic quantum phenomenon characterised by unique properties such as frictionless flow, high thermal conductivity and the presence of quantised vortices. Our study focuses on what is arguably the most well-known attribute: the ability for an object to move through a superfluid without experiencing a drag force when travelling below a threshold critical velocity.The Landau criterion for superfluidity predicts the critical velocity in a BEC is equal to the speed of sound, and this conclusion is supported by a large body of theoretical work. However, a number of experiments have observed lower critical velocities than theory predicts. In the first part of this thesis, we numerically model experiments on the superfluid critical velocity of an elongated, harmonically trapped Bose-Einstein condensate as reported by [P. Engels and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007)]. These experiments swept a repulsive obstacle, formed by a optical dipole potential, through the long axis of a condensate at constant velocity. Their results found an increase in the resulting density fluctuations of the condensate above an obstacle velocity of v _ 0:3 mm s