The formalism based on the equal-time Wigner function of the two-point correlation function for a quantized Klein–Gordon field is presented. The notion of the gauge-invariant Wigner transform is introduced and equations for the corresponding phase-space calculus are formulated. The equations of motion governing the Wigner function of the Klein–Gordon field are derived. It is shown that they lea...

A technique for studying collisionless dynamics of a homogeneous superconducting system is developed which is based on Riccati parametrization of the Wigner distribution function. The quantum evolution of the superconducting order parameter, initially deviating from the equilibrium value, is calculated using this technique. The effect of a time-dependent BCS paring interaction on the dynamics o...

Phase space representations have proven their value in classical mechanics and ever since the work of Wigner [1] in quantum mechanics as well. The map introduced by Wigner from state functions to quasi-probability functions is notable for two fundamental properties. The first reason it is notable relates to the fact that, in general, the Wigner quasi-probability function is not everywhere nonne...

Recently there has been renewed interest in applications of the so-called phase-space formulation of quantum mechanics’) for both equilibrium2) and non-equilibrium phenomena3). Its basic feature is to provide a framework for the treatment of quantum mechanical problems in terms of classical phasespace language. Following the appearance of the well-known Wigner distribution function’), many othe...

An intriguing aspect of quantum mechanics is the intricate description of the state of a physical system. Therefore, a great deal of interest has been attracted by the recent experimental demonstration that the quantum state of a simple system, namely a single light mode, can be completely characterized in a feasible scheme [1]. The measurement was based on an observation that marginals of the ...

We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint.

The nonclassicality of photon-added coherent fields in the thermal channel is investigated by exploring the volume of the negative part of the Wigner function which reduces with the dissipative time. The Wigner functions become positive when the decay time exceeds a threshold value. For the case of the single photon-added coherent state, we derive the exact threshold values of decay time in the...