Truncated Wigner approximation as a non-positive Kraus map - Klimov, A B; Sainz, I; Romero, J L (arXiv.org, 2021)
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.