تقرير
Numerical simulation of the Gross-Pitaevskii equation via vortex tracking
| العنوان: | Numerical simulation of the Gross-Pitaevskii equation via vortex tracking |
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| المؤلفون: | Corso, Thiago Carvalho, Kemlin, Gaspard, Melcher, Christof, Stamm, Benjamin |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | This paper deals with the numerical simulation of the Gross-Pitaevskii (GP) equation, for which a well-known feature is the appearance of quantized vortices with core size of the order of a small parameter $\varepsilon$. Without a magnetic field and with suitable initial conditions, these vortices interact, in the singular limit $\varepsilon\to0$, through an explicit Hamiltonian dynamics. Using this analytical framework, we develop and analyze a numerical strategy based on the reduced-order Hamiltonian system to efficiently simulate the infinite-dimensional GP equation for small, but finite, $\varepsilon$. This method allows us to avoid numerical stability issues in solving the GP equation, where small values of $\varepsilon$ typically require very fine meshes and time steps. We also provide a mathematical justification of our method in terms of rigorous error estimates of the error in the supercurrent, together with numerical illustrations. |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2404.02133Test |
| رقم الانضمام: | edsarx.2404.02133 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |