出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：We discuss how dynamical fermion computations may be made yet cheaper by using symplectic
integrators that conserve energy much more accurately without decreasing the integration step
size. We first explain why symplectic integrators exactly conserve a “shadow” Hamiltonian close
to the desired one, and how this Hamiltonian may be computed in terms of Poisson brackets. We
then discuss how classical mechanics may be implemented on Lie groups and derive the form of
the Poisson brackets and force terms for some interesting integrators such as those making use of
second derivatives of the action (Hessian or force gradient integrators). We hope that these will
be seen to greatly improve energy conservation for only a small additional cost and that their use
will significantly reduce the cost of dynamical fermion computations.
