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A Comparison of the Properties of Superconductors and Superfluid Helium
Published in R. D. Parks, Superconductivity, 2018
Let us begin with a pure uncharged superfluid, such as liquid helium, at T = 0. In this case we know that the fluid flow will be governed by Eq. (5), which has a form identical with that governing the flow of a classical inviscid fluid. We may therefore expect that a quantum vortex will move like its classical analogue, i.e., that in a steady state each part of each vortex core will move with the local superfluid velocity (generated by, e.g., other vortices or other parts of the same vortex).
Wave–vortex interactions and effective mean forces: three basic problems
Published in Geophysical & Astrophysical Fluid Dynamics, 2020
The dilution effect summarised by (15) is key to understanding the noninterchangeability of limits in problem (ii). For instance, the same dilution effect occurs for any unrefracted wavetrain whose width W is given an arbitrary fixed value while its length , whether or not it overlaps the vortex core. When it does overlap, the local Stokes drift contributes to while the diluted return flow is still governed by (15), going to zero in the limit. It remains zero if the limit is taken subsequently. Therefore, for problem (ii) in the limit followed by , the formulae (12) and (14) are replaced by and Not only the magnitudes but also the signs have changed. Notice again that (17) is equal to the Craik–Leibovich vortex force integrated over the vortex core, corresponding to what is called the Iordanskii force in the quantum vortex literature (e.g. Sonin 1997, Stone 2000), with corresponding to the phonon current per unit mass.
Qubit unitary lattice algorithm for spin-2 Bose–Einstein Condensates. I – Theory and Pade initial conditions
Published in Radiation Effects and Defects in Solids, 2020
George Vahala, Linda Vahala, Min Soe
Here is the BEC wave function and, in condensed matter jargon, is the order parameter for the phase transition to a BEC state (5). gives the strength of the boson–boson s-wave interaction and is the chemical potential. As vortices play a critical role in classical fluid turbulence, so quantum vortices play a very important role in BECs and in the rotation of the condensed state (2). For a scalar BEC, these vortices must satisfy the U(1) rotational symmetry of a circle since the order parameter must be single-valued (4). Thus if one encircles a vortex (rotation angle ), the order parameter must be periodic and this yields a Madelung representation of the wave function For , the density at the scalar vortex core must be zero: i.e. the scalar vortex is a topological singularity of the order parameter field, with at the vortex core. Moreover, the circulation about a quantum vortex core must be quantized in units of , where M is the mass of the alkali gas (4).