We introduce a two-dimensional active nematic with quenched disorder. We write the coarse-grained hydrodynamic equations of motion for slow variables, viz. density and orientation. Disorder strength is tuned from zero to large values. Results from the numerical solution of equations of motion as well as the calculation of two-point orientation correlation function using linear approximation shows that the ordered steady state follows a disorder dependent crossover from quasi-long-range order to short-range order. Such crossover is due to the pinning of $\pm 1/2$ topological defects in the presence of finite disorder, which breaks the system in uncorrelated domains. Finite disorder slows the dynamics of $+1/2$ defect, and it leads to slower growth dynamics. The two-point correlation functions for the density and orientation fields show good dynamic scaling but no static scaling for the different disorder strengths. Our findings can motivate experimentalists to verify the results and find applications in living and artificial apolar systems in the presence of a quenched disorder.

• Received 3 March 2020
• Revised 27 July 2020
• Accepted 2 November 2020

DOI:https://doi.org/10.1103/PhysRevE.102.052609