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Symplectic vector space
About: Symplectic vector space is a research topic. Over the lifetime, 2048 publications have been published within this topic receiving 53456 citations.
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TL;DR: This work considers the computation of the Iwasawa decomposition of a symplectic matrix via the QR factorization and improves on the method recently described by T.-Y.
25 citations
TL;DR: In this article, the existence of traces for star products on a symplectic manifold has been shown for arbitrary star products with respect to a normalisation introduced by Karabegov [Lett. Math. Phys. 45 (1998) 217].
25 citations
TL;DR: In this paper, the Wisdom-Holman midpoint scheme with corrector and corrector for higher order schemes is derived and a scheme of order O(eh6) + (e2h2), where e is the order of perturbation and h the stepsize.
Abstract: In this paper we consider almost integrable systems for which we show that there is a direct connection between symplectic methods and conventional numerical integration schemes. This enables us to construct several symplectic schemes of varying order. We further show that the symplectic correctors, which formally remove all errors of first order in the perturbation, are directly related to the Euler—McLaurin summation formula. Thus we can construct correctors for these higher order symplectic schemes. Using this formalism we derive the Wisdom—Holman midpoint scheme with corrector and correctors for higher order schemes. We then show that for the same amount of computation we can devise a scheme which is of order O(eh6) + (e2h2), where e is the order of perturbation and h the stepsize. Inclusion of a modified potential further reduces the error to O(eh6) + (e2h4).
25 citations
TL;DR: In this paper, the quantum analogues of the first and second fundamental theorem for vector invariants for the symplectic group were established for a vector space V endowed with a non degenerate antisymmetric bilinear form.
25 citations
25 citations