Quantization Of Circulation Research Articles

Phenomenology of transition to quantum turbulence in flows of superfluid helium

Transition from laminar to turbulent states of classical viscous fluids is complex and incompletely understood. Transition to quantum turbulence (QT), by which we mean the turbulent motion of quantum fluids such as helium II, whose physical properties depend on quantum physics in some crucial respects, is naturally more complex. This increased complexity arises from superfluidity, quantization of circulation, and, at finite temperatures below the critical, the two-fluid behavior. Transition to QT could involve, as an initial step, the transition of the classical component, or the intrinsic or extrinsic nucleation of quantized vortices in the superfluid component, or a simultaneous occurrence of both scenarios—and the subsequent interconnected evolution. In spite of the multiplicity of scenarios, aspects of transition to QT can be understood at a phenomenological level on the basis of some general principles, and compared meaningfully with transition in classical flows.

Reply to "Comment on 'Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory' ".

We refute the criticism expressed in a Comment by Krstulovic, L'vov, and Nazarenko [Phys. Rev. E 105, 027101 (2022)10.1103/PhysRevE.105.027101] on our paper [Phys. Rev. E 103, 023106 (2021)2470-004510.1103/PhysRevE.103.023106]. We first show that quantization of circulation is not ignored in our analysis. Then, we propose a more sophisticated analysis to avoid a subtle problem with the regularity of the velocity field. We thus defend the main results of our paper, which predicts the double-cascade scenario where the quantum stress cascade follows the Richardson cascade. We also provide a conjecture on the relation between the Kelvin-wave cascade and the quantum stress cascade.

Comment on "Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory".

In a recent paper, Tanogami [Phys. Rev. E 103, 023106 (2021)2470-004510.1103/PhysRevE.103.023106] proposes a scenario for quantum turbulence where the energy spectrum at scales smaller than the intervortex distance is dominated by a quantum stress cascade, in opposition to Kelvin-wave cascade predictions. The purpose of the present Comment is to highlight some physical issues in the derivation of the quantum stress cascade, in particular to stress that quantization of circulation has been ignored.

Dynamics of a Vortex Lattice in an Expanding Polariton Quantum Fluid.

If a quantum fluid is driven with enough angular momentum, at equilibrium the ground state of the system is given by a lattice of quantized vortices whose density is prescribed by the quantization of circulation. We report on the first experimental study of the Feynman-Onsager relation in a nonequilibrium polariton fluid, free to expand and rotate. Upon initially imprinting a lattice of vortices in the quantum fluid, we track the vortex core positions on picosecond timescales. We observe an accelerated stretching of the lattice and an outward bending of the linear trajectories of the vortices, due to the repulsive polariton interactions. Access to the full density and phase fields allows us to detect a small deviation from the Feynman-Onsager rule in terms of a transverse velocity component, due to the density gradient of the fluid envelope acting on the vortex lattice.

Stability of the quantized circulation of an attractive Bose-Einstein condensate in a rotating torus

We investigate rotational properties of a system of bosons with attractive interactions confined in a one-dimensional torus. Two kinds of ground states, uniform-density and bright-soliton states, are obtained analytically as functions of the strength of interaction and of the rotational frequency of the torus. The quantization of circulation appears in the uniform-density state, but disappears upon formation of the soliton. By comparison with the results of exact diagonalization of the many-body Hamiltonian, we show that the Bogoliubov theory is valid at absolute zero over a wide range of parameters. At finite temperature we employ the exact diagonalization method to examine how thermal fluctuations smear the plateaus of the quantized circulation. Finally, by rotating the system with an axisymmetry-breaking potential, we clarify the process in which the quantized circulation becomes thermodynamically stabilized.

Off-Diagonal Long-Range Order in Bose Liquids: Irrotational Flow and Quantization of Circulation

On the basis of gauge invariance, it is proven in an elementary and straightforward manner, but without invoking any ad hoc assumption, that the existence of off-diagonal long-range order in one-particle reduced density matrix in Bose liquids implies both the irrotational flow in a simply connected region and the quantization of circulation in a multiply connected region, the two fundamental properties of a Bose superfluid. The origin for both is the phase coherence of condensate wave functions. Some relevant issues are also addressed.

Exact solution for superfluid film vortices on a torus.

The problem of describing the velocity field of quantized vortices on a torus is solved exactly by use of Riemann's bilinear relations of 1857. The solution is used to discuss the behavior of superfluids on porous media. The close connection between topology and quantization of circulation is emphasized as well as its implications for a successful theory of the experiments.

New experiments on quantization of circulation in superfluid4He

We measure circulation in superfluid4He around a thin vibrating wire which can serve as the core of a vortex. As well as confirming earlier measurements of the quantum of circulation, our data yield new information on the dynamics of transitions between stable circulation states. A situation in which a vortex line partially detaches from the wire, with the free end precessing about the wire, is observed.

Algebraic topology and the quantization of circulation in superfluid helium.

Onsager's argument for the quantization of circulation in superfluid helium is reconsidered in light of current discussions of quantum mechanics in multiply connected spaces (Aharanov-Bohm effect, fractional statistics, etc.). We find that there is no a priori reason to exclude multiple-valued functions of the order parameter. This results in circulation levels that still exhibit quantized changes of size h/m, but their absolute values are no longer integer multiples of this quantum of circulation. The implications of this theory for experiments using the Vinen vibrating-wire technique are discussed.

Galilean presymmetry and the quantization of circulation

A theorem of Jauch is used to establish symmetry properties of the free energy of the state of persistent circular flow. The quantization of circulation is shown to follow for equilibrium flow states.

Mass currents and singularities in3He-A

It is shown that the particular form of the mass current in 3He-A found by Cross (1975) is equivalent to a phenomenological assumption that the current depends only on the traceless part of the tensor Omega ij introduced by Mermin and Ho (1976) to describe spatial variations of the order parameter. An equation of motion for Omega ij is derived in terms of the vector C introduced previously by the author (1975) to describe temporal variations of the order parameter. The appropriate generalizations of curl nu s=0 and the quantization of circulation for 3He-A are derived in terms of Omega ij, and the nature of possible singularities is discussed.

Galilean covariance of gauge fields and quantization of circulation in He II

Galilean covariance of gauge fields and quantization of circulation in He II

Quantization of Circulation in Superfluid Helium

Quantization of Circulation in Superfluid Helium

Quantization of Circulation and Torque in Superfluid Helium

Quantization of Circulation and Torque in Superfluid Helium

Evidence for the Quantization of Circulation in Liquid Helium II

Evidence for the Quantization of Circulation in Liquid Helium II