## On the exact unitary integration of time-varying quantum Liouville equations

### Claudio Altafini

* Rendiconti del Seminario Matematico dell'Universita e del Politecnico di Torino*, 63(4):9-18, 2005.

In this paper, the Dyson series corresponding to the time-varying Hamiltonian of a finite dimensional quantum mechanical system is expanded in terms of products of exponentials of a complete basis of commutator superoperators in the corresponding Liouville space.
The Cayley-Hamilton theorem and the Wei-Norman formula allow to express explicitly the functional relation between the Dyson series and the product of exponentials via a set of first order differential equations.
Since the method is structure preserving, it can be used for the exact unitary integration of the driven Liouville-von Neumann equation.

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