# Dynamics of dissipative topological defects in coupled phase oscillators

## TL;DR

This paper investigates how dissipative topological defects evolve in coupled phase oscillators, revealing that defect dynamics depend on coupling rates and influence system coherence, with implications for understanding phase transitions.

## Contribution

It introduces a numerical study of defect dynamics in coupled oscillators, highlighting the impact of coupling rate on defect number and system order, connecting to the Kibble-Zurek mechanism.

## Key findings

- Faster coupling rates lead to fewer topological defects.
- Defect number scales with the coupling rate, similar to KZM.
- Reducing defects enhances long-term coherence and system order.

## Abstract

The dynamics of dissipative topological defects in a system of coupled phase oscillators, arranged in one and two-dimensional arrays, is numerically investigated using the Kuramoto model. After an initial rapid decay of the number of topological defects, due to vortex-anti-vortex annihilation, we identify a long-time (quasi) steady state where the number of defects is nearly constant. We find that the number of topological defects at long times is significantly smaller when the coupling between the oscillators is increased at a finite rate rather than suddenly turned on. Moreover, the number of topological defects scales with the coupling rate, analogous to the cooling rate in KibbleZurek mechanism (KZM). Similar to the KZM, the dynamics of topological defects is governed by two competing time scales: the dissipation rate and the coupling rate. Reducing the number of topological defects improves the long time coherence and order parameter of the system and enhances its probability to reach a global minimal loss state that can be mapped to the ground state of a classical XY spin Hamiltonian.