Transmission eigenvalue distribution in disordered media from radiant field theory

We develop a field-theoretic framework, called radiant field theory, to calculate the distribution of transmission eigenvalues for coherent wave propagation in disordered media. At its core is a self-consistent transport equation for a $2\times 2$ matrix radiance, reminiscent of the radiative transfer equation but capable of capturing coherent interference effects. This framework goes beyond the limitations of the Dorokhov-Mello-Pereyra-Kumar theory by accounting for both quasiballistic and diffusive regimes. It also handles open geometries inaccessible to standard wave-equation solvers such as infinite slabs. Analytical and numerical solutions are provided for these geometries, highlighting in particular the impact of the waveguide shape and the grazing modes on the transmission eigenvalue distribution in the quasiballistic regime. By removing the macroscopic assumptions of random matrix models, this microscopic theory enables the calculation of transmission statistics in regimes previously out of reach. It also provides a foundation for exploring more complex observables and physical effects relevant to wavefront shaping in realistic disordered systems.