Strong fluctuation theory of Tatarskii: quantum field theoretic approach – a critical assessment

Abstract

In this paper, we carried out a critical investigation of the strong fluctuation theory using a quantum field theoretic approach [Tatarskii VI. The effects of the turbulent atmosphere on wave propagation. Jerusalem: IPST; 1971]. We employed the Dyson and Bethe-Salpeter equations to derive the radiative transfer equation (RTE) for the Green's function of the radiant intensity. We proceeded to obtain estimates of the domain of validity of the RTE. The results thus obtained satisfy both the optical theorem for waves in random media and energy conservation. We also derived the RTE for our problem by employing a recently developed scale-separated asymptotic theory [Bal G., Komorowski T, Ryzhik L. Kinetic limits of waves in random media. Kinet Relat Models. 2010;3:529–644]. Although the RTE obtained by the two approaches are identical, we explain that the applicability regimes, and hence validity conditions are different.

Keywords:

• Quantum field theoretic approach
• strong fluctuation theory
• scale-separated asymptotics
• radiative transfer equations
• random media

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 ${\hat{D}}_1$ and ${\hat{D}}_2$ are Dyson operators (cf. (3(3) $\hat{D}{G}_m=-\delta (\mathbf{\text{r}}-{\mathbf{\text{r}}}^{\prime })$(3) )) corresponding to spatial variables ${\mathbf{\text{r}}}_1$ and ${\mathbf{\text{r}}}_2$, respectively.

2 by directly employing the governing equations of scaled Green's functions and their Wigner transforms