Boltzmann-Ginzburg-Landau theory for autochemotaxis of active rod-like particles

We investigate the interplay between chemotaxis and alignment interactions in active rod-like particles, such as E. coli and Janus rods. Starting from a discrete model of self-propelled rods with chemotactic responses, we employ a Boltzmann-Ginzburg-Landau (BGL) approach to derive coarse-grained dynamical equations for the density, polar and nematic orientational order parameters, and the concentration field of the chemoattractant. We perform a linear stability analysis for fluctuations around uniform steady states corresponding to isotropic and nematic phases. In both phases, we find that translational chemotactic response promotes instability, while rotational chemotactic response suppresses it, elucidating their contrasting effects on the onset of collective dynamics.