J. Bajer, P. Lisonek,
Symbolic computation approach to nonlinear dynamics.
Journal of Modern Optics 38 (1991), 719-729.

The description and demonstration of short-time approximation method are presented for solution of Heisenberg equation using a computer for operator algebra symbolic computation to obtain operator series. Multimode nonlinear processes can be studied by this method in fully quantum way, the symbolic operator or standard numerical results as well as the graphical dependences can be gained from the computer. Although a meaning of the method can be seen in its ability to improve essentially the numerical predictions rather than to discover new states or effects, we have obtained squeezing parameters and variances of photon number for initially squeezed states (and some other cases) in degenerate parametric process.


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