Hamiltonian Dynamics and Structural States of Two-Dimensional Active Particles

We show that a two-dimensional system of flocking active particles interacting hydrodynamically can be expressed using a Hamiltonian formalism. The Hamiltonian depends strictly on the angles between the particles and their orientation, thereby restricting their available phase-space. Simulations of co-oriented active particles evolve into "escalators"- sharp lines at a particular tilt along which particles circulate. The conservation of the Hamiltonian and its symmetry germinate the self-assembly of the observed steady-state arrangements as confirmed by stability analysis.