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Modified Form of Wigner Functions for Non-Hamiltonian Systems

Quantization of non-Hamiltonian systems (such as damped systems) often gives rise to complex spectra and corresponding resonant states, therefore a standard form calculating Wigner functions cannot lead to static quasi-probability distribution functions. We show that a modified form of the Wigner functions satisfies a ∗-genvalue equation and can be derived from deformation quantization for such systems.