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Symmetric decomposition of exponential operators and evolution problems

✍ Scribed by G. Dattoli; L. Giannessi; M. Quattromini; A. Torre

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
608 KB
Volume
111
Category
Article
ISSN
0167-2789

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✦ Synopsis

Symplectic integrators are numerical schemes for autonomous Hamiltonian systems that preserve exactly the phase space structure (i.e. Poincar6 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.

πŸ“œ SIMILAR VOLUMES

Spectral Decomposition of Symmetric Oper
Spectral Decomposition of Symmetric Operator Matrices
✍ Reinhard Mennicken; Andrey A. Shkalikov πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 649 KB

The authors study symmetric operator matrices A B = ( B ' C ) in the product of Hilbert spaces H = Hi xH2, where the entries are not necessarily bounded operators. Under suitable assumptions the closure Lo exists and is a selfadjoint operator in H. With Lo, the closure of the transfer function M(X)