The Wigner-Function Approach to Quantum Transport

Abstract

Wigner introduced the function that carries his name in 1932 [472, 473] as an instrument to study quantum corrections to classical statistical mechanics. Even though the Wigner function (WF) cannot be strictly interpreted as a probability density, as demonstrated by the fact that it can assume negative values (see for example [439]), the very fact that it is defined in a phase space, together with its main properties and dynamical equation, makes it particularly useful to study quantum corrections to classical results and the classical limit to quantum physics. The WF has been widely employed in several fields of quantum statistical physics, such as molecular, atomic, and nuclear physics, quantum optics, quantum chemistry, quantum entanglement and entropy [496]. As it regards the use of the WF in electron transport, it has received great attention since the 1980s, when technological improvements required the development of a full quantum theory of electronic transport.