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This theoretical study examines how pairs of quantized vortices behave in fluid systems confined to doubly periodic domains (torus geometry) when energy dissipation is present. The researchers found that vortex pairs with the same rotation direction spiral outward, while opposite-rotating pairs collapse in finite time, but the toroidal geometry induces unexpected angular drift that wouldn't occur in flat space. Notably, dissipative unequal opposite-sign vortex pairs produce a unique frequency-doubling chirp pattern that differs fundamentally from analogous inspiral phenomena in electromagnetic and gravitational wave systems.
Why it matters
These findings are relevant for understanding vortex dynamics in superfluid systems at finite temperatures and could inform predictions about quantum turbulence behavior in confined geometries. The analytical solutions and geometric corrections identified may help refine models of rotating superfluids in experimental setups and improve understanding of dissipative processes in quantum fluids.
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arXiv:2604.23857v2 Announce Type: replace
Abstract: We study a dissipative extension of vortex-binary motion in a doubly periodic fluid domain. The underlying conservative system admits an exact integrable reduction to a single complex relative coordinate. Dissipation is introduced via a minimal rotated-velocity (mutual-friction) term, as motivated by finite-temperature superfluid dynamics, converting the Hamiltonian evolution into a mixed symplectic–gradient flow with monotonic energy decay for quantized vortices. In the local regime, the dissipative binary remains analytically solvable and admits closed-form solutions, with systematic corrections arising from the toroidal geometry. Equal same-sign vortices execute outward spiraling motion, while equal opposite-sign pairs (dipoles) undergo finite-time collapse in the planar limit. On the torus, however, the dipole orientation is no longer invariant: the geometry induces a slow angular drift, even in regimes where planar dynamics would preserve alignment. For unequal opposite-sign pairs, dissipation induces coupled contraction and rotation, leading to a finite-time nonlinear chirp characterized by $dot{omega}proptoomega^2$, in contrast with electromagnetic and gravitational inspirals where $dot{omega}propto omega^{3}$ and $dot{omega}propto omega^{11/3}$. These results highlight the interplay between Hamiltonian structure, dissipation, and geometry in periodic fluid systems.
Source: Dissipative Vortex Binaries in Compact Fluid Domains with Geometric Corrections