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Journal of Low Temperature Physics

Thermodynamic Equilibrium Vortices in Counterflowing Superfluid: Calculation of Partition Function

Sergey K. Nemirovskii

Published Jan 31, 2022• 4 citations
Publisher
DOI
10.1007/s10909-021-02661-0

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Vortex dynamics in superfluid systems

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Abstract Based on the theory of the thermodynamic equilibrium in a system of quantum vortices in superfluid liquids and in a Bose – Einstein condensate in the presence of a counterflow of normal and superfluid components, we investigate the structure of a chaotic tangle of quantum vortices in turbulent superfluid liquids. Using the characteristic functional method, the properties of hydrodynamic vortex filaments are examined. It is shown that the average curvature of the vortex lines is on the order of the intervortex distance, with the proportionality coefficient being independent of the counterflow velocity. It is found that the degree of anisotropy of the vortex loops does not depend on the applied counterflow velocity. The obtained results explain the origin of the anisotropy as well as the relationship between the curvature of the lines and the intervortex space and their dependence on the parameters of the problem.
Rotating supersolids challenge the conventional notion of superfluid flow: quantized vortices coexist with crystalline order arising from the system's intrinsic density modulation. Drawing on concepts developed in the context of superfluid helium, this seemingly paradoxical state is often described phenomenologically in terms of a dual response, combining superfluid flow with rigid-body-like motion. Here we show that these apparently distinct behaviors emerge from a single microscopic velocity field, globally constrained by irrotationality. By applying a Helmholtz decomposition, we disentangle a divergence-free incompressible component, which carries vortex circulation, from a curl-free compressible component generated by the intrinsic density modulation. In absence of vortices, the response is entirely encoded in the compressible field: the droplets co-rotate with the external drive, while the interstitial fluid develops an oppositely directed counterflow that preserves vanishing circulation. Above the vortex nucleation threshold, the incompressible component carries the usual quantized circulation, whereas the compressible field counteracts the vortex-induced angular momentum, reducing the total jump with respect to an unmodulated condensate. Our results recast supersolid rotation in terms of a flow-counterflow response, providing a microscopic interpretation of the phenomenological rigid/superfluid partitioning.
The equations of motion of vortices in an ideal two-dimensional fluid are derived, and the laws of conservation associated with the motion are discussed. Two regions of flow are considered, an infinite region and a region bounded on the outside by a circle. The kinetic energy and angular momentum of a vortex fluid in these two regions are calculated. A Lagrangian formalism is introduced in order to discuss the symmetry transformations of vortex systems and their associated conservation laws. The kinematic stability of rigidly rotating polygonal configurations of quantized vortices is determined, and the states of thermodynamic equilibrium of a rotating superfluid are found for low angular velocities, resulting in the calculation of the spectrum of critical angular velocities for the creation of one, two, and three vortices.