Dynamics of the τ-Wigner distribution function

Abstract

Some of the non-classical distribution functions defined on the phase space can be unified owing to specific parameterization. The latter allows one to think about the general form of the equation of motion for such parameterized distribution functions. Motivated by this idea, we derive the equation of motion for so-called the τ-Wigner distribution function. This parameterization directly results from a modification of the linear transformation of the spatial variables which is used to derive the original Wigner distribution function and its equation of motion. The derived equation is analytically solved for the case of linear potential. The point symmetries of this last equation are also analysed.

Dynamical entropic measure of nonclassicality of phase-dependent family of Schrödinger cat states

“…The assumption of the purity of the state is significantly important because it allows us to look at the WDF as the amplitude of the probability density in the phase space according to the arguments presented in Refs. 39 , 41 , i.e. the WDF represents the wave function on the phase space for the pure state being a particular solution of the Schrödinger equation written in the phase-space representation.…”

“…The negativity of the WDF has been the subject of numerous discussions and interpretations. Among these various proposals, the approach assuming that the WDF is treated as a wave function defined on the phase space deserves special attention 39 – 41 . The immediate consequence of this approach is an interpretation of this function as the probability amplitude on the phase space.…”