تقرير
A new fast numerical method for the generalized Rosen-Zener model
| العنوان: | A new fast numerical method for the generalized Rosen-Zener model |
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| المؤلفون: | Bonhomme, Christian, Pozza, Stefano, Van Buggenhout, Niel |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | In quantum mechanics, the Rosen-Zener model represents a two-level quantum system. Its generalization to multiple degenerate sets of states leads to larger non-autonomous linear system of ordinary differential equations (ODEs). We propose a new method for computing the solution operator of this system of ODEs. This new method is based on a recently introduced expression of the solution in terms of an infinite matrix equation, which can be efficiently approximated by combining truncation, fixed point iterations, and low-rank approximation. This expression is possible thanks to the so-called $\star$-product approach for linear ODEs. In the numerical experiments, the new method's computing time scales linearly with the model's size. We provide a first partial explanation of this linear behavior. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.04144 |
| رقم الأكسشن: | edsarx.2311.04144 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |