Dynamical cooling driven by self-similar fronts in the 2D nonlinear Schrödinger model
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911657781886976 |
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| author | Laurie, Jason Thalabard, Simon Nazarenko, Sergey |
| author_facet | Laurie, Jason Thalabard, Simon Nazarenko, Sergey |
| contents | We analyze the dynamics towards partial thermalization and subsequent cooling in the defocusing two-dimensional nonlinear Schrödinger model, using direct simulations and insights from the wave-kinetic equations (WKE) and a fourth-order differential approximation model (DAM). We show that the evolving WKE spectrum exhibits two distinct similarity ranges--the quasi-thermal core and the ultraviolet tail--whereas in the DAM, an additional range of infrared self-similarity appears. By stretching the quasi-thermal region, the self-similar fronts drive an effective dynamical cooling process towards the formal but ill-defined equilibrium state at vanishing temperature--analogous to an ultraviolet catastrophe in a system of classical waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06396 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamical cooling driven by self-similar fronts in the 2D nonlinear Schrödinger model Laurie, Jason Thalabard, Simon Nazarenko, Sergey Mathematical Physics Statistical Mechanics Fluid Dynamics Optics We analyze the dynamics towards partial thermalization and subsequent cooling in the defocusing two-dimensional nonlinear Schrödinger model, using direct simulations and insights from the wave-kinetic equations (WKE) and a fourth-order differential approximation model (DAM). We show that the evolving WKE spectrum exhibits two distinct similarity ranges--the quasi-thermal core and the ultraviolet tail--whereas in the DAM, an additional range of infrared self-similarity appears. By stretching the quasi-thermal region, the self-similar fronts drive an effective dynamical cooling process towards the formal but ill-defined equilibrium state at vanishing temperature--analogous to an ultraviolet catastrophe in a system of classical waves. |
| title | Dynamical cooling driven by self-similar fronts in the 2D nonlinear Schrödinger model |
| topic | Mathematical Physics Statistical Mechanics Fluid Dynamics Optics |
| url | https://arxiv.org/abs/2605.06396 |