Introduction to the special issue on Wigner functions

The Wigner function was first derived by E.P. Wigner around 1931 as an exotic outcome of the wave mechanics which, being defined in the phase space, does not favor either coordinate or momentum variables. Pioneered by H.J. Groenewold and J.E.Moyal theWigner formulation of quantum mechanics evolved until the end of last century, to a fully autonomous, independent alternative to Hilbert space mechanics and path integral formulations. As S. MacLane put it (Ladies and) gentlemen: There is lots of room left in Hilbert Space, the same holds true for the phase space, where Wigner and alternative approaches, likeHusimi andBohmian distributions, are easily accommodated. Applied to challenges in computational electronics, the Wigner approach offers the unique ability to describe transient problems for open systems by simultaneously accounting for different levels of approximation for the effects of the degrees of freedom associated with the environment. For example, the Wigner–Boltzmann equation enables the formalism with the efficient Boltzmann model of collisions (local in position/time) with phonons and impurities featuring the classical era of microelectronics. The equation bridges the gap between classical and quantum electron dynamics, ensuring a seamless transition between coherent and scattering dominated modes of transport. This approach