Abstract:
The dynamics of topological defects in a system of coupled phase oscillators, arranged in one
and two-dimensional arrays, was numerically investigated using the Kuramoto model. After a
rapid decay of the number of topological defects, a long-time quasi steady state with few
topological defects was detected. Two competing time scales governed the dynamics
corresponding to the dissipation rate and the coupling quench rate. The density of topological
defects scales as a power law function of the coupling quench rate ρ ∼ Cν with ν = 0.25.
Reducing the number of topological defects improves the long time coherence and order
parameter of the system, enhancing the probability to reach a global minimal loss state that can
be mapped to the ground state of a classical XY spin Hamiltonian.
