A Geometrical Method of Decoupling

Details A Geometrical Method of Decoupling A Geometrical Method of Decoupling

2012-01-04

arxiv.org/abs/1201.0907v1

Physics

Mathematical Physics

12 pages, 1 figure

Scientific paper

In a preceeding paper the real Dirac matrices have been introduced to coupled linear optics and a recipe to decouple positive definite Hamiltonians has been given. In this article a geometrical method is presented which allows to decouple regular {\it and} irregular systems with the same straightforward method and to compute the eigenvalues and eigenvectors of Hamiltonian matrices with both, real and imaginary eigenvalues. It is shown that the algebraic decoupling is closely related to a geometric "decoupling" by the orthogonalization of the vectors $\vec E$, $\vec B$ and $\vec p$, that were introduced with the so-called "electromechanical equivalence" (EMEQ). When used iteratively, the decoupling algorithm can also be applied to n-dimensional non-dissipative systems.

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