Symplectic integrators are numerical schemes for autonomous Hamiltonian systems that preserve exactly the phase space structure (i.e. Poincaré invariants). Conservation of symplectic structure is connected to fundamental properties of evolution of mechanical systems both in classical realm (Liouville Theorem) as well as in the quantum domain (unitarity of evolution operator). The interest in these methods stems from the fact that they are free from a number of problems affecting other time-proven algorithms. In this paper we prove that symmetric split operator technique (SSOT) can be exploited to obtain naturally symplectic integrators of arbitrarily high order with very little programming effort. Examples of application to charged beam transport and quantum optics are given. Copyright © 1998 Elsevier Science B.V. All rights reserved.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Condensed Matter Physics
Dattoli, G., Giannessi, L., Quattromini, M., & Torre, A. (1998). Symmetric decomposition of exponential operators and evolution problems. Physica D: Nonlinear Phenomena, 111(1-4), 129 - 142. https://doi.org/10.1016/S0167-2789(97)80008-5