Out of Equilibrium Behaviour of Quantum Vortices: A Comparison of Point Vortex Dynamics and Fokker-Planck Evolution
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| Format: | Preprint |
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2025
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| _version_ | 1866917957152538624 |
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| author | Tattersall, R. J. Baggaley, A. W. Billam, T. P. |
| author_facet | Tattersall, R. J. Baggaley, A. W. Billam, T. P. |
| contents | 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, approximately less than -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 two for energy per vortex approximately greater than -4 to one which depends explicitly on the initial conditions for energy per vortex approximately less than -5. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_11286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Out of Equilibrium Behaviour of Quantum Vortices: A Comparison of Point Vortex Dynamics and Fokker-Planck Evolution Tattersall, R. J. Baggaley, A. W. Billam, T. P. Quantum Gases 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, approximately less than -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 two for energy per vortex approximately greater than -4 to one which depends explicitly on the initial conditions for energy per vortex approximately less than -5. |
| title | Out of Equilibrium Behaviour of Quantum Vortices: A Comparison of Point Vortex Dynamics and Fokker-Planck Evolution |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2503.11286 |