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.