Topic
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.
Papers published on a yearly basis
Papers
More filters
TL;DR: An explicit and symplectic integrator for quantum-classical molecular dynamics is presented in this article, where the integration scheme is time reversible and unitary in the quantum part, and it is shown that the PickABACK algorithm is more stable and accurate at no additional numerical effort.
43 citations
TL;DR: In this article, the authors define Symplectic cohomology groups for a class of symplectic fibrations with closed symplectic base and convex at infinity fiber, and prove new cases of the Weinstein conjecture.
Abstract: We define Symplectic cohomology groups for a class of symplectic fibrations with closed symplectic base and convex at infinity fiber. The crucial geometric assumption on the fibration is a negativity property reminiscent of negative curvature in complex vector bundles. When the base is symplectically aspherical we construct a spectral sequence of Leray-Serre type converging to the Symplectic cohomology groups of the total space, and we use it to prove new cases of the Weinstein conjecture.
43 citations
43 citations
TL;DR: In this article, a decomposition of the nuclear Hubert space into collective subspaces and symplectic shells is proposed, and the resultant symplectic shell model is shown to provide a basis for microscopic calculations which are immediately interpretable in collective-model terms.
43 citations
TL;DR: In this paper, it was shown that the Fano variety of a cubic in P^5 and the double cover of an EPW sextic is made of 28 isolated fixed points and 1 K3 surface.
Abstract: Let X be a holomorphic symplectic fourfold such that b_2=23 and i a symplectic involution of X . The fixed locus F of i is a smooth symplectic submanifold of X; we show that F contains at least 12 isolated points and 1 smooth surface. We conjecture that F is made of 28 isolated fixed points and 1 K3 surface and we provide evidences for the conjecture in some examples, as the Hilbert scheme of a K3 surface, the Fano variety of a cubic in P^5 and the double cover of an EPW sextic.
43 citations