Stationary Veselov-Novikov equation and isothermally asymptotic surfaces in projective differential geometry

In the strong localization regime, light confined to a well-defined volume of space by the mutual interference of its countless constituent scattered waves can be expected to acquire unusual characteristics. These include a vanishing momentum, an effective tensorial rest mass, and "photonic atom recoil." Impurity atoms that emit light under these conditions should consist of coupled atom-cavity systems with energy densities extending over regions larger than the atoms, but smaller than a cubic wavelength, in which radiant transport is suppressed by near-field correlated scattering. This unusual regime is now accessible over broad wavelength ranges in random nanoparticle media, opening the way to studies of novel phenomena such as strong localization phase transitions, lasers without cavities, and optical energy storage.