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arXiv · 2108.04189

Truncated Wigner approximation as a non-positive Kraus map

A. B. Klimov·I. Sainz·J. L. Romero
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Abstract

We show that the Truncated Wigner Approximation developed in the flat phase-space is mapped into a Lindblad-type evolution with an indefinite metric in the space of linear operators. As a result, the classically evolved Wigner function corresponds to a non-positive operator $\hat{R}(t)$, which does not describe a physical state. The rate of appearance of negative eigenvalues of $\hat{R}(t)$ can be efficiently estimated. The short-time dynamics of the Kerr and second harmonic generation Hamiltonains are discussed.

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A. B. Klimov, I. Sainz, J. L. Romero. 2021-08-09. Truncated Wigner approximation as a non-positive Kraus map. https://doi.org/10.1088/1402-4896%2Fab8d53

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