Insights into the semiclassical Wigner treatment of bimolecular collisions

Abstract

The semiclassical Wigner treatment of bimolecular collisions, proposed by Lee and Scully on a partly intuitive basis [J. Chem. Phys. 73, 2238(1980], is derived here from first principles. The derivation combines E. J. Heller's ideas [J. Chem. Phys. 62, 1544(1975 65, 1289(1976 75, 186 (1981)], the backward picture of molecular collisions [L. Bonnet, J. Chem. Phys. 133, 174108 (2010)] and the microreversibility principle.

On the formation of the equation of state of an evolving quantum field

“…We see that the LO approximation in φ q corresponds to averaging over initial conditions for classical trajectory with the weight given by the corresponding Wigner function. Expression (16) was earlier derived by different meth ods in [4,7], see also [8] and [10,11]. For spatially inhomogeneous fields (16) is replaced by (17) where Ᏸφ(x) and Ᏸφ(x) mean the integration over 4 and 3 dimensional functions, respectively, and…”

“…The problem of formation of equation of state was analyzed, at an example of scalar field theory, in [4,5,6]. The analysis was based on the fact that summation of leading quantum corrections can be cast in the form of integration over initial conditions for classical trajectories with the weight given by the Wigner function, see [7] and, in different contexts, [8,9,10,11].…”

Applicability of the Wigner functional approach to evolution of quantum fields

“…CSA is based on the fact that summation of leading quantum corrections can be cast in the form of integration over initial conditions for classical trajectories with the weight given by the Wigner functional. It is interesting to note that similar approach was used in atomic and chemical physics [23], [24].…”

Quantum corrections to the classical statistical approximation for the expanding quantum field

“…The Keldysh-Schwinger (KS) technique (closed-time path formalism) [19,18] provides a systematic way of studying time-dependent nonequilibrium phenomena in quantum field theory, see the recent review in [3]. Within this formalism, the CSA (averaging over classical trajectories with different initial conditions) does naturally arise at the leading order of the semiclassical approximation [20,21]. In the quantum field theory context this was discussed in [30] where the JIMWLK equations [26,27,28,29] were shown to follow from such a semiclassical expansion.…”