Abstract
In his celebrated 1932 paper, Eugene Wigner computed "quantum corrections" to the classical Maxwell-Botzmann equilibrium distribution. The method he used was based on the representation of quantum states as pseudo-distributions in phase space. This "phase space representation of quantum mechanics" is today an active research field not only for theoretical reasons but also for applied purposes. Indeed, this classical-looking formalism finds its perfect application to systems, such as modern nano-devices, that lie at the border between classical and quantum behavior. Another interesting feature is the possibility to borrow mathematical tools from classical kinetic theory.
In this talk we briefly introduce Wigner's formalism and its relations with Boltzmann's kinetic theory, and present some recent applications to quantum diffusion and hydrodynamics.
