SYMMETRICAL DECOMPOSITION OF EXPONENTIAL OPERATORS AND EVOLUTION PROBLEMS

Symplectic integrators are numerical schemes for autonomous Hamiltonia n systems that preserve exactly the phase space structure (i.e. Poinca re invariants), Conservation of symplectic structure is connected to f undamental properties of evolution of mechanical systems both in class ical realm (Liouville Theorem) as well as in the quantum domain (unita rity 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 op erator technique (SSOT) can be exploited to obtain naturally symplecti c integrators of arbitrarily high order with very little programming e ffort. Examples of application to charged beam transport and quantum o ptics are given.