Superfluid Dynamics Research Articles

Derrick’s theorem beyond a potential

Scalar field theories with derivative interactions are known to possess solitonic excitations, but such solitons are generally unsatisfactory because the effective theory fails precisely where nonlinearities responsible for the solitons are important. A new class of theories possessing (internal) galilean invariance can in principle bypass this difficulty. Here, we show that these galileon theories do not possess stable solitonic solutions. As a by-product, we show that no stable solitons exist for a different class of derivatively coupled theories, describing for instance the infrared dynamics of superfluids, fluids, solids and some k-essence models.

Dissipative superfluid dynamics from gravity

Charged asymptotically AdS 5 black branes are sometimes unstable to the condensation of charged scalar fields. For fields of infinite charge and squared mass −4 Herzog was able to analytically determine the phase transition temperature and compute the endpoint of this instability in the neighborhood of the phase transition. We generalize Herzog’s construction by perturbing away from infinite charge in an expansion in inverse charge and use the solutions so obtained as input for the fluid gravity map. Our tube wise construction of patched up locally hairy black brane solutions yields a one to one map from the space of solutions of superfluid dynamics to the long wavelength solutions of the Einstein Maxwell system. We obtain explicit expressions for the metric, gauge field and scalar field dual to an arbitrary superfluid flow at first order in the derivative expansion. Our construction allows us to read off the the leading dissipative corrections to the perfect superfluid stress tensor, current and Josephson equations. A general framework for dissipative superfluid dynamics was worked out by Landau and Lifshitz for zero superfluid velocity and generalized to nonzero fluid velocity by Clark and Putterman. Our gravitational results do not fit into the 13 parameter Clark-Putterman framework. Purely within fluid dynamics we present a consistent new generalization of Clark and Putterman’s equations to a set of superfluid equations parameterized by 14 dissipative parameters. The results of our gravitational calculation fit perfectly into this enlarged framework. In particular we compute all the dissipative constants for the gravitational superfluid.

Size and dynamics of vortex dipoles in dilute Bose-Einstein condensates

Recently, Freilich et al. [Science 329, 1182 (2010)] experimentally discovered stationary states of vortex dipoles, pairs of vortices of opposite circulation, in dilute Bose-Einstein condensates. To explain their observations, we perform simulations based on the Gross-Pitaevskii equation and obtain excellent quantitative agreement on the size of the stationary dipole. We also investigate how their imaging method, in which atoms are repeatedly extracted from a single condensate, affects the vortex dynamics. We find that it mainly induces isotropic size oscillations of the condensate without otherwise disturbing the vortex trajectories. Thus, the imaging technique appears to be a promising tool for studying real-time superfluid dynamics.

Nonstationary Superconductivity: Quantum Dissipation and Time-Dependent Ginzburg-Landau Equation

Transport equations of the macroscopic superfluid dynamics are revised on the basis of a combination of the conventional (stationary) Ginzburg-Landau equation and Schrödinger's equation for the macroscopic wave function (often called the order parameter) by using the well-known Madelung-Feynman approach to representation of the quantum-mechanical equations in hydrodynamic form. Such an approach has given (a) three different contributions to the resulting chemical potential for the superfluid component, (b) a general hydrodynamic equation of superfluid motion, (c) the continuity equation for superfluid flow with a relaxation term involving the phenomenological parameters and , (d) a new version of the time-dependent Ginzburg-Landau equation for the modulus of the order parameter which takes into account dissipation effects and reflects the charge conservation property for the superfluid component. The conventional Ginzburg-Landau equation also follows from our continuity equation as a particular case of stationarity. All the results obtained are mutually consistent within the scope of the chosen phenomenological description and, being model-neutral, applicable to both the low- and high- superconductors.

Spreading of superfluid vorticity clouds in normal-fluid turbulence

In this paper, we formulate a self-consistent model of thermal superfluid dynamics. By solving it, we analyse the problem of superfluid vorticity cloud propagation in normal-fluid turbulence. We show that superfluid cloud expansion is driven by pattern-forming superfluid vortex instabilities taking place in the interface layer between the cloud's bulk and the outer undisturbed normal-fluid turbulence. The radius of the cloud increases linearly with time. Mutual friction transfers energy from the normal-fluid turbulence to the superfluid cloud, whilst damping the smallest normal-fluid turbulence motions. This damping action is much weaker than viscous dissipation effects in a corresponding pure normal-fluid turbulence. The energy spectrum of superfluid turbulence presents the k−3 scaling that characterizes the spiral superfluid vorticity patterns of normal vortex tube–superfluid vortex interactions. The corresponding k−2 pressure spectrum signifies the singular nature of superfluid vorticity. These two scalings coincide in wavenumber space with the Kolmogorov regime in the normal-fluid turbulence. We compute a fractal dimension df ≈ 1.652 for superfluid vorticity. Due to simpler underlying superfluid vortex dynamics in relation to the strongly nonlinear classical vortex dynamics, this fractal dimension is smaller than the corresponding dimension of vortex tube centrelines in classical turbulence.

Vortices, Superfluid Dynamics, and Quantum Turbulence

Vortices, Superfluid Dynamics, and Quantum Turbulence

Quantum Turbulence: Achievements and Challenges

The paper is, for the most part, a review, written in its original form for an International Workshop on Vortices, Superfluid Dynamics, and Quantum Turbulence, held in Lammi, Finland, in 2010. Achievements are reviewed, and a strong emphasis is placed on problems that are either unsolved or still the subject of active discussion. These problems often call for more powerful experimental techniques, including local probes and actual visualization of the turbulent motion. Special emphasis is placed on recent progress in the development of visualization.

Superfluid Dynamics in Neutron Star Crusts

A simple description of superfluid hydrodynamics in the inner crust of a neutron star is given. Particular attention is paid to the effect of the lattice of nuclei on the properties of the superfluid neutrons, and the effects of entrainment, the fact that some fraction of the neutrons are locked to the motion of the protons in nuclei.

Fission-fragment and neutron data traced back to the macroscopic and microscopic properties of the fissioning systems

A new model description of fission-fragment yields and prompt neutron emission is developed. The yields of the different fission channels and their properties are attributed to the number of relevant states above the potential-energy landscape on the fission path at the moment of dynamical freeze-out, which is specific to the collective coordinate considered. The model combines well established ideas with novel concepts. The separability principle of macroscopic properties of the compound nucleus and microscopic properties of the fragments strongly reduces the number of model parameters and assures a high predictive power. The recently discovered energy-sorting mechanism in superfluid nuclear dynamics determines the sharing of intrinsic excitation energy at scission and the enhancement of even-odd structure in asymmetric splits.

Wave–Vortex Interactions in Fluids and Superfluids

This article reviews the methods of wave–mean interaction theory for classical fluid dynamics, and for geophysical fluid dynamics in particular, providing a few examples for illustration. It attempts to bring the relevant equations into their simplest possible form, which highlights the organizing role of the circulation theorem in the theory. This is juxtaposed with a simple account of superfluid dynamics and the attendant wave–vortex interactions as they arise in the nonlinear Schrödinger equation. Here the fundamental physical situation is more complex than in the geophysical case, and the current mathematical understanding is more tentative. Classical interaction theory might be put to good use in the theoretical and numerical study of quantum fluid dynamics.

Elementary Vortex Processes in Thermal Superfluid Turbulence

By solving pertinent mathematical models with numerical and computational methods, we analyze the formation of superfluid vorticity structures in a turbulent normal fluid with an inertial range exhibiting Kolmogorov scaling. We demonstrate that mutual friction forcing causes quantum vortex instabilities whose signature is spiral vortical configurations. The spirals expand until they accidentally meet metastable, intense normal fluid vorticity tubes of similar curvature and vorticity orientation that trap them by driving them towards low mutual friction sites where superfluid bundles are formed. The bundle formation sites are located within the tube cores, but, due to tube curvature and many-tube interaction effects, are displaced by variable distances from the tube centerlines as they follow the contours of the latter. We analyze possible implications of these processes in fully developed thermal superfluid turbulence dynamics.

Vortex-antivortex pair in a Bose-Einstein condensate

Presented is a type-II quantum algorithm for superfluid dynamics, used to numerically predict solutions of the GP equation for a complex scalar field (spinless bosons) in φ4 theory. The GP equation is a long wavelength effective field theory of a microscopic quantum lattice gas with nonlinear state reduction. The quantum lattice gas algorithm for modeling the dynamics of the one-body BEC state in 3+1 dimensions is presented. To demonstrate the method's strength as a computational physics tool, a difficult situation of filamentary singularities is simulated, the dynamics of solitary vortex-antivortex pairs, which are a basic building block of morphologies of quantum turbulence.

Superfluid Bose-Fermi mixture from weak coupling to unitarity

We investigate the zero-temperature properties of a superfluid Bose-Fermi mixture by introducing a set of coupled Galilei-invariant nonlinear Schr\"odinger equations valid from weak coupling to unitarity. The Bose dynamics is described by a Gross-Pitaevskii-type equation including beyond-mean-field corrections possessing the correct weak-coupling and unitarity limits. The dynamics of the two-component Fermi superfluid is described by a density-functional equation including beyond-mean-field terms with correct weak-coupling and unitarity limits. The present set of equations is equivalent to the equations of generalized superfluid hydrodynamics, which take into account also surface effects. The equations describe the mixture properly as the Bose-Bose repulsive (positive) and Fermi-Fermi attractive (negative) scattering lengths are varied from zero to infinity in the presence of a Bose-Fermi interaction. The present model is tested numerically as the Bose-Bose and Fermi-Fermi scattering lengths are varied over wide ranges covering the weak-coupling to unitarity transition.

Superfluid properties of a Bose–Einstein condensate in an optical lattice confined in a cavity

We study the effect of a one dimensional optical lattice in a cavity field with quantum properties on the superfluid dynamics of a Bose–Einstein condensate (BEC). In the cavity the influence of atomic backaction and the external driving pump become important and modify the optical potential. Due to the coupling between the condensate wavefunction and the cavity modes, the cavity light field develops a band structure. This study reveals that the pump and the cavity emerges as a new handle to control the superfluid properties of the BEC.

Relaxation of superfluid vortex bundles via energy transfer to the normal fluid

We apply numerical and computational analyses to the decay of a topologically nontrivial, bundle-structured superfluid vortex tangle via mutual friction effected energy transfer to an initially stationary, viscous normal fluid. We demonstrate that, as long as the coherent superfluid vorticity structures remain intact, the induced normal-fluid vorticity acquires a similar to the superfluid vorticity morphology, and the normal-fluid energy spectrum mimics the superfluid energy spectrum presenting a low-wavenumber scaling regime. After a (smaller than the integral advective time scale) transient, the superfluid vorticity bundles disintegrate; this is followed by the decay of normal-fluid energy. The kinetic energies of the two fluids are mismatched throughout the decay period, and the dismantling of coherent vorticity destroys the low-wavenumber energy spectrum scaling in both fluids. At the point of maximum normal-fluid energy, the circulation of the induced normal-fluid vortices is comparable to the ''macroscopic'' circulation of the superfluid vorticity bundles. We show that the superfluid dynamics are dominated throughout the decay period by inertial rather than mutual friction effects, that the formation of bundlelike coherent superfluid vortices cannot be the outcome of pure (reconnecting) Biot-Savart dynamics, and that superfluid vortex length dynamics are not analogous to superfluid energy dynamics. We conjecture that themore » dynamics of fully developed, turbulent thermal superfluid flow could be described in terms of interactions of cyclic coherent vorticity patterns in both fluids.« less

Non-equilibrium coherence dynamics in one-dimensional Bose gases

Low-dimensional systems provide beautiful examples of many-body quantum physics. For one-dimensional (1D) systems, the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.

Modelling the dynamics of superfluid neutron stars

In this brief summary I describe our recent work on superfluid neutron star dynamics. I review results on shear viscosity, hyperon bulk viscosity, vortex mediated mutual friction and the modelling of multifluid systems in general. For each problem I provide a set of questions that need to be addressed by future work.

Superfluid dynamics of a Bose–Einstein condensate in a one-dimensional optical superlattice

We derive and study the Bloch and Bogoliubov spectrum of a Bose–Einstein condensate (BEC) confined in a one-dimensional optical superlattice (created by interference between a primary optical lattice and a secondary optical lattice of small strength), using the Bogoliubov approximation and the hydrodynamic theory with mode coupling. We show that a BEC in an optical superlattice experiences two different tunnelling parameters and hence behaves like a diatomic chain. We derive expressions for the tunnelling parameters as a function of the strength of the primary and secondary lattice. This gives rise to a gapped branch in addition to the gapless acoustical branch in the Bogoliubov spectrum. The spectrum strongly depends on the strength of the secondary lattice, the interaction parameter and the number density of atoms. The effective mass is found to increase as the depth of the secondary optical lattice increases, a property that was utilized in Paraedes et al (2004 Nature 429 277) to achieve the Tonks–Girardeau regime. The coupling between the inhomogeneous density in the radial plane and the density modulation along the optical lattice gives rise to a multibranch Bogoliubov spectrum.

Time-dependent Ginzburg-Landau theory for atomic Fermi gases near the BCS-BEC crossover

We construct a time-dependent Ginzburg-Landau (TDGL) theory for the superfluid atomic Fermi-gases near the Feshbach resonance from the fermion-boson model on the basis of the functional integral formalism. We show that the GL coefficients in the TDGL equation are complex numbers except in the BEC limit. The complex TDGL equation describes both damping and propagating dynamics, which leads to very rich superfluid dynamics near the Feshbach resonance. We predict multiple plane-wave modes corresponding to the in-phase and out-of-phase like oscillations between fermionic and bosonic superfluids and a galaxylike spiral pattern for a vortex.

Quantum dynamics, particle delocalization and instability of Mott states: the effect of fermion–boson conversion on Mott states

We study the quantum dynamics of superfluids of bosons hybridized with Cooper pairs near Feshbach resonances and the influence of fermion–boson conversion on Mott states. We derive a set of equations of motion which describe novel low energy dynamics in superfluids and obtain a new distinct branch of gapped collective modes in superfluids which involve anti-symmetric phase oscillations in fermionic and bosonic channels. We also find that Mott states in general are unstable with respect to fermion–boson conversion; particles become delocalized and the off-diagonal long-range order of superfluids can be developed when a finite conversion is present. We further point out a possible hidden order in Mott states. It is shown that the quantum dynamics of Fermi–Bose states can be characterized by either an effective coupled U(1) ⊗ U(1) quantum rotor Hamiltonian in a large-N limit or a coupled XXZ ⊗ XXZ spin Hamiltonian in a single-orbit limit.