Markovian evolution of Gaussian states in the semiclassical limit

Details Markovian evolution of Gaussian states in the semiclassical limit Markovian evolution of Gaussian states in the semiclassical limit

2008-08-16

arxiv.org/abs/0808.2258v3

Physics

Quantum Physics

10 pages. Reason for replacement: the article was split into two parts: the first part about WKB was incomplete and led to an

Scientific paper

We derive an approximate Gaussian solution of the Lindblad equation in the semiclassical limit, given a general Hamiltonian and linear coupling with the environment. The theory is carried out in the chord representation and describes the evolved quantum characteristic function, which gives direct access to the Wigner function and the position representation of the density operator by Fourier transforms. The propagation is based on a system of non-linear equations taking place in a double phase space, which coincides with Heller's theory of unitary evolution of Gaussian wave packets when the Lindbladian part is zero.

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