An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications
| dc.creator | Casas, Fernando | |
| dc.creator | Murua, Ander | |
| dc.date | 2008-10-15 | |
| dc.date.accessioned | 2026-07-07T13:02:03Z | |
| dc.date.available | 2026-07-07T13:02:03Z | |
| dc.description | We provide a new algorithm for generating the Baker--Campbell--Hausdorff (BCH) series $Z = \log(\e^X \e^Y)$ in an arbitrary generalized Hall basis of the free Lie algebra $\mathcal{L}(X,Y)$ generated by $X$ and $Y$. It is based on the close relationship of $\mathcal{L}(X,Y)$ with a Lie algebraic structure of labeled rooted trees. With this algorithm, the computation of the BCH series up to degree 20 (111013 independent elements in $\mathcal{L}(X,Y)$) takes less than 15 minutes on a personal computer and requires 1.5 GBytes of memory. We also address the issue of the convergence of the series, providing an optimal convergence domain when $X$ and $Y$ are real or complex matrices. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/0810.2656 | |
| dc.identifier | http://arxiv.org/abs/0810.2656 | |
| dc.identifier | Journal of Mathematical Physics 50 (2009), 033513 | |
| dc.identifier | doi:10.1063/1.3078418 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226354 | |
| dc.subject | Mathematical Physics | |
| dc.title | An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications | |
| dc.type | text |