A symplectic integrator for molecular dynamics on a hypersphere

J.-M. Caillol
2020 Condensed Matter Physics  
We present a reversible and symplectic algorithm called ROLL, for integrating the equations of motion in molecular dynamics simulations of simple fluids on a hypersphere S d of arbitrary dimension d. It is derived in the framework of geometric algebra and shown to be mathematically equivalent to algorithm RATTLE. An application to molecular dynamics simulation of the one component plasma is briefly discussed. Classical mechanics in an euclidean space of arbitrary dimension General discussion
more » ... neral discussion Let us first fix some definitions and notations. We associate to the usual inner product space R d the euclidean affine space E d , defined as a set of points M such that, given an origin O, there is a unique vector q ∈ R d such that − − → OM = q. Once O is fixed, we identify the two spaces E d and R d . We denote by {e i }, i = 1, . . . , n, the standard orthonormal basis of E d with the property that e i · e j = δ i j , where "·" is the usual scalar product of R d and δ i j the Kronecker symbol. This work is licensed under a Creative Commons Attribution 4.0 International License . Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. 23603-1 J.-M. Caillol 1GA is a relatively new concept, with a lot of applications in many branches of physics, robotics and engineering. G d is a Clifford algebra, the elements of which are called multi-vectors which represent subspaces of R n . The reader not acquainted with this subject will find a digest in appendix A and much more details in the recent review by A. Macdonald [8] and his remarkably clear elementary textbook [9] . At a more advanced level, the reader should consult references [5, 7, 10] . For applications to physics, the books [6, 10] will be consulted with profit. We adopt the notations and definitions of Macdonald throughout this paper. 23603-2
doi:10.5488/cmp.23.23603 fatcat:ucfmnujsbzbplngufomi6rjp7q