Universality in driven systems with a multiply-degenerate umbilic point

We investigate a driven particle system, a multilane asymmetric exclusion process, where the particle number in every lane is conserved, and stationary state is fully uncorrelated. The phase space has, starting from three lanes and more, an umbilic manifold where characteristic velocities of all the modes but one coincide, thus allowing us to study a weakly hyperbolic system with arbitrarily large degeneracy. We then study space-time fluctuations in the steady state, at the umbilic manifold, which are expected to exhibit universal scaling features. We formulate an effective mode-coupling theory (MCT) for the multilane model within the umbilic subspace and test its predictions. Unlike in the bidirectional two-lane model with an umbilic point studied earlier, here we find a robust $z=3/2$ dynamical exponent for the umbilic mode. The umbilic scaling function, obtained from Monte-Carlo simulations appears to have a universal shape for a range of interaction parameters and depends only on umbilic mode degeneracy. Remarkably, the shape and dynamic exponent of the non-degenerate mode can be analytically predicted on the base of effective MCT, up to non-universal scaling factor. Our findings suggest the existence of novel universality classes with dynamical exponent $3/2$, appearing in long-lived hydrodynamic modes with equal characteristic velocities.