1202.3628 (Denys I. Bondar et al.)

Wigner Function's Negativity Demystified    [PDF]

Denys I. Bondar, Renan Cabrera, Herschel A. Rabitz

As early as 1932 Wigner defined the joint distribution for the coordinate and
momentum of a quantum particle. Despite a drawback of being sometimes negative,
the Wigner distribution has stood the test of time and found many applications.
Having demonstrated that the Wigner function of a pure quantum state is a wave
function in the specially tuned Dirac bra-ket formalism, we argue that the
Wigner function is in fact a probability amplitude for the quantum particle to
be at a certain point of the classical phase space. Since probability amplitude
need not be positive, our findings elucidate the long-standing mystery of the
Wigner function's negativity. Additionally, we establish that in the classical
limit, the Wigner function transforms into a classical Koopman-von Neumann wave
function rather than into a classical probability distribution. As a result,
contrary to widespread beliefs, the volume of negative regions in the Wigner
distribution cannot quantify the degree of quantum character.

View original: http://arxiv.org/abs/1202.3628