Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1912.09535 · Physical Review Research

Universal dynamics in the expansion of vortex clusters in a dissipative two-dimensional superfluid

Oliver R. Stockdale, Matthew T. Reeves, Xiaoquan Yu, Guillaume Gauthier, K. H. Lee, Warwick P. Bowen, Tyler W. Neely, Matthew J. Davis

Published Jul 24, 2020• 19 citations
arXivHTMLPDF

Abstract

This work uncovers a new universality class in the out-of-equilibrium dynamics of vortices in finite temperature, two-dimensional superfluids. The authors show that any initial vortex distribution expands to form a uniform cluster - a process that is forbidden in viscous, classical fluids.
DOI
10.1103/physrevresearch.2.033138

Related papers

Universal dynamics in the expansion of vortex clusters in a dissipative two-dimensional superfluid

Oliver R. Stockdale, Matthew T. Reeves, Xiaoquan Yu +5 more

A large ensemble of quantum vortices in a superfluid may itself be treated as a novel kind of fluid that exhibits anomalous hydrodynamics. Here we consider the dynamics of vortex clusters under thermal friction and present an analytic solution that uncovers a new universality class in the out-of-equilibrium dynamics of dissipative superfluids. We find that the long-time dynamics of the vorticity distribution is universal in the form of an expanding Rankine vortex (i.e., top-hat distribution) independent of initial conditions. This highlights a fundamentally different decay process to classical fluids, where the Rankine vortex is forbidden by viscous diffusion. Numerical simulations of large ensembles of point vortices confirm the universal expansion dynamics and further reveal the emergence of a frustrated lattice structure marked by strong correlations. We present experimental results of expanding vortex clusters in a quasi-two-dimensional Bose-Einstein condensate that are in excellent agreement with the vortex fluid theory predictions, demonstrating that the signatures of vortex fluid theory can be observed with as few as N∼11 vortices. Our theoretical, numerical, and experimental results establish the validity of the vortex fluid theory for superfluid systems.

Bulletin of the American Physical Society•Mar 18, 2021•0 citations

Dynamics of vortex cluster crystallisation and single-vortex pinning in two-dimensional superfluids

Oliver R. Stockdale

In this thesis, we analytically and numerically study two different scenarios of vortex dynamics in a two-dimensional superfluid. The first system we explore is an expanding cluster of like-sign vortices, which recently suggested it could explain observations in a superfluid optomechanics experiment. We employ a recent theoretical model that approximates large collections of vortices as a fluid and present an analytic solution for its dynamics. Analysis suggests that as a cluster expands due to thermal friction, it forms a Rankine vortex (i.e., a top-hat distribution) that expands self-similarly in time regardless of initial vorticity distribution. Numerical simulations of point vortices confirm this universal expanding regime and further demonstrates vortex lattice formation that goes beyond the vortex fluid theory. We analyse correlations that emerge in the resulting lattices and observe decaying disorder as the cluster expands. Furthermore, we analyse experimental data from a quasi-two-dimensional 87Rb Bose-Einstein condensate, which supports the vortex fluid theory’s predictions.The second scenario considers the dynamics of a scattering event where a single quantum vortex interacts with a uniform, circular pinning potential in a steady two-dimensional superfluid flow. We first develop an approximate hydrodynamical model to understand the interaction between the vortex and the pinning potential in the conservative regime and find it is in good agreement with the mean-field Gross-Pitaevskii equation in the low-velocity limit. We further solve the Gross-Pitaevskii equation for higher background velocities to study how the vortex moves around pinning sites, interacts with it, and ultimately becomes pinned. We uncover four different regimes of vortex pinning, each marked with a characteristic emission of sound energy. Finally, we study how vortices become unpinned from a pinning site, revealing large vortex dipoles form to stabilise the system.Our work in this thesis takes significant steps towards advancing knowledge of both the collective dynamics of vortices and their individual interaction with defects upon surface substrates. Our numerical and analytical results opens up new avenues of exploration be it further understanding dissipation mechanisms in two-dimensional superfluids, or elucidating the nature of vortex pinning in systems such as neutron stars.

•Mar 1, 2021•0 citations

Out-of-equilibrium behavior of quantum vortices: A comparison of point vortex dynamics and Fokker-Planck evolution

R. J. Tattersall, Andrew William Baggaley, T. P. Billam

An out-of-equilibrium two-dimensional superfluid relaxes towards equilibrium via a process of coarsening, driven by the annihilation of vortices with antivortices. Here we present a comparison of two different numerical models of this process, a dissipative point vortex model and Fokker-Planck evolution, across a wide range of initial configurations and levels of dissipation. We find that our dissipative point vortex model is well approximated by Fokker-Planck evolution only for very low initial energies per vortex, E 0 / N v ≲ − 4 , when almost all vortices and antivortices are closely bound into dipoles. We observe that the dynamical critical exponent z in the dissipative point vortex model undergoes a crossover, from a roughly constant value close to 2 for E 0 / N v ≳ − 4 , to a value which depends explicitly on the initial conditions for E 0 / N v ≲ − 5 .

arXiv:2503.11286•Physical Review A•Jun 9, 2025•0 citations

Out-of-equilibrium behavior of quantum vortices: A comparison of point vortex dynamics and Fokker-Planck evolution

Richard Tattersall, Andrew William Baggaley, T. P. Billam

© (2025) (American Physical Society) All rights reserved.An out-of-equilibrium two-dimensional superfluid relaxes towards equilibrium via a process of coarsening, driven by the annihilation of vortices with antivortices. Here we present a comparison of two different numerical models of this process, a dissipative point vortex model and Fokker-Planck evolution, across a wide range of initial configurations and levels of dissipation. We find that our dissipative point vortex model is well approximated by Fokker-Planck evolution only for very low initial energies per vortex, E0/Nv −4, when almost all vortices and antivortices are closely bound into dipoles. We observe that the dynamical critical exponent z in the dissipative point vortex model undergoes a crossover, from a roughly constant value close to 2 for E0/Nv −4, to a value which depends explicitly on the initial conditions for E0/Nv −5.

•Jan 1, 2025•0 citations

Out-of-equilibrium behavior of quantum vortices: A comparison of point vortex dynamics and Fokker-Planck evolution

Richard Tattersall, Andrew William Baggaley, T. P. Billam

© (2025) (American Physical Society) All rights reserved.An out-of-equilibrium two-dimensional superfluid relaxes towards equilibrium via a process of coarsening, driven by the annihilation of vortices with antivortices. Here we present a comparison of two different numerical models of this process, a dissipative point vortex model and Fokker-Planck evolution, across a wide range of initial configurations and levels of dissipation. We find that our dissipative point vortex model is well approximated by Fokker-Planck evolution only for very low initial energies per vortex, E0/Nv −4, when almost all vortices and antivortices are closely bound into dipoles. We observe that the dynamical critical exponent z in the dissipative point vortex model undergoes a crossover, from a roughly constant value close to 2 for E0/Nv −4, to a value which depends explicitly on the initial conditions for E0/Nv −5.

•Jul 22, 2025•0 citations

Vortex Thermometry for Turbulent Two-Dimensional Fluids

Andrew J. Groszek, Matthew J. Davis, David M. Paganin +2 more

We introduce a new method of statistical analysis to characterize the dynamics of turbulent fluids in two dimensions. We establish that, in equilibrium, the vortex distributions can be uniquely connected to the temperature of the vortex gas, and we apply this vortex thermometry to characterize simulations of decaying superfluid turbulence. We confirm the hypothesis of vortex evaporative heating leading to Onsager vortices proposed in Phys. Rev. Lett. 113, 165302 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.165302, and we find previously unidentified vortex power-law distributions that emerge from the dynamics.

arXiv:1702.05229•Physical Review Letters•Jan 19, 2018•30 citations
A large ensemble of quantum vortices in a superfluid may itself be treated as a novel kind of fluid that exhibits anomalous hydrodynamics. Here we consider the dynamics of vortex clusters under thermal friction and present an analytic solution that uncovers a new universality class in the out-of-equilibrium dynamics of dissipative superfluids. We find that the long-time dynamics of the vorticity distribution is universal in the form of an expanding Rankine vortex (i.e., top-hat distribution) independent of initial conditions. This highlights a fundamentally different decay process to classical fluids, where the Rankine vortex is forbidden by viscous diffusion. Numerical simulations of large ensembles of point vortices confirm the universal expansion dynamics and further reveal the emergence of a frustrated lattice structure marked by strong correlations. We present experimental results of expanding vortex clusters in a quasi-two-dimensional Bose-Einstein condensate that are in excellent agreement with the vortex fluid theory predictions, demonstrating that the signatures of vortex fluid theory can be observed with as few as N∼11 vortices. Our theoretical, numerical, and experimental results establish the validity of the vortex fluid theory for superfluid systems.
In this thesis, we analytically and numerically study two different scenarios of vortex dynamics in a two-dimensional superfluid. The first system we explore is an expanding cluster of like-sign vortices, which recently suggested it could explain observations in a superfluid optomechanics experiment. We employ a recent theoretical model that approximates large collections of vortices as a fluid and present an analytic solution for its dynamics. Analysis suggests that as a cluster expands due to thermal friction, it forms a Rankine vortex (i.e., a top-hat distribution) that expands self-similarly in time regardless of initial vorticity distribution. Numerical simulations of point vortices confirm this universal expanding regime and further demonstrates vortex lattice formation that goes beyond the vortex fluid theory. We analyse correlations that emerge in the resulting lattices and observe decaying disorder as the cluster expands. Furthermore, we analyse experimental data from a quasi-two-dimensional 87Rb Bose-Einstein condensate, which supports the vortex fluid theory’s predictions.The second scenario considers the dynamics of a scattering event where a single quantum vortex interacts with a uniform, circular pinning potential in a steady two-dimensional superfluid flow. We first develop an approximate hydrodynamical model to understand the interaction between the vortex and the pinning potential in the conservative regime and find it is in good agreement with the mean-field Gross-Pitaevskii equation in the low-velocity limit. We further solve the Gross-Pitaevskii equation for higher background velocities to study how the vortex moves around pinning sites, interacts with it, and ultimately becomes pinned. We uncover four different regimes of vortex pinning, each marked with a characteristic emission of sound energy. Finally, we study how vortices become unpinned from a pinning site, revealing large vortex dipoles form to stabilise the system.Our work in this thesis takes significant steps towards advancing knowledge of both the collective dynamics of vortices and their individual interaction with defects upon surface substrates. Our numerical and analytical results opens up new avenues of exploration be it further understanding dissipation mechanisms in two-dimensional superfluids, or elucidating the nature of vortex pinning in systems such as neutron stars.
An out-of-equilibrium two-dimensional superfluid relaxes towards equilibrium via a process of coarsening, driven by the annihilation of vortices with antivortices. Here we present a comparison of two different numerical models of this process, a dissipative point vortex model and Fokker-Planck evolution, across a wide range of initial configurations and levels of dissipation. We find that our dissipative point vortex model is well approximated by Fokker-Planck evolution only for very low initial energies per vortex, E 0 / N v ≲ − 4 , when almost all vortices and antivortices are closely bound into dipoles. We observe that the dynamical critical exponent z in the dissipative point vortex model undergoes a crossover, from a roughly constant value close to 2 for E 0 / N v ≳ − 4 , to a value which depends explicitly on the initial conditions for E 0 / N v ≲ − 5 .
© (2025) (American Physical Society) All rights reserved.An out-of-equilibrium two-dimensional superfluid relaxes towards equilibrium via a process of coarsening, driven by the annihilation of vortices with antivortices. Here we present a comparison of two different numerical models of this process, a dissipative point vortex model and Fokker-Planck evolution, across a wide range of initial configurations and levels of dissipation. We find that our dissipative point vortex model is well approximated by Fokker-Planck evolution only for very low initial energies per vortex, E0/Nv −4, when almost all vortices and antivortices are closely bound into dipoles. We observe that the dynamical critical exponent z in the dissipative point vortex model undergoes a crossover, from a roughly constant value close to 2 for E0/Nv −4, to a value which depends explicitly on the initial conditions for E0/Nv −5.
© (2025) (American Physical Society) All rights reserved.An out-of-equilibrium two-dimensional superfluid relaxes towards equilibrium via a process of coarsening, driven by the annihilation of vortices with antivortices. Here we present a comparison of two different numerical models of this process, a dissipative point vortex model and Fokker-Planck evolution, across a wide range of initial configurations and levels of dissipation. We find that our dissipative point vortex model is well approximated by Fokker-Planck evolution only for very low initial energies per vortex, E0/Nv −4, when almost all vortices and antivortices are closely bound into dipoles. We observe that the dynamical critical exponent z in the dissipative point vortex model undergoes a crossover, from a roughly constant value close to 2 for E0/Nv −4, to a value which depends explicitly on the initial conditions for E0/Nv −5.
We introduce a new method of statistical analysis to characterize the dynamics of turbulent fluids in two dimensions. We establish that, in equilibrium, the vortex distributions can be uniquely connected to the temperature of the vortex gas, and we apply this vortex thermometry to characterize simulations of decaying superfluid turbulence. We confirm the hypothesis of vortex evaporative heating leading to Onsager vortices proposed in Phys. Rev. Lett. 113, 165302 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.165302, and we find previously unidentified vortex power-law distributions that emerge from the dynamics.