Phase ordering percolation and an infinite domain wall in segregating binary Bose-Einstein condensates

TL;DR

This paper applies percolation theory to analyze phase transition dynamics and domain pattern formation in segregating binary Bose-Einstein condensates, revealing universal scaling behaviors and properties of infinite domain walls.

Contribution

It introduces a finite-size-scaling analysis of percolation thresholds and demonstrates the universal scaling function for percolation probability in binary condensates.

Findings

Percolation threshold near 0.5 for strongly repulsive condensates.

Universal scaling function describes percolation probability.

Infinite domain wall exhibits noninteger fractal dimension and maintains scaling behavior.

Abstract

Percolation theory is applied to the phase-transition dynamics of domain pattern formation in segregating binary Bose--Einstein condensates in quasi-two-dimensional systems. Our finite-size-scaling analysis shows that the percolation threshold of the initial domain pattern emerging from the dynamic instability is close to 0.5 for strongly repulsive condensates. The percolation probability is universally described with a scaling function when the probability is rescaled by the characteristic domain size in the dynamic scaling regime of the phase-ordering kinetics, independent of the intercomponent interaction. It is revealed that an infinite domain wall sandwiched between percolating domains in the two condensates has an noninteger fractal dimension and keeps the scaling behavior during the dynamic scaling regime. This result seems to be in contrast to the argument that the dynamic scale invariance is violated in the presence of an infinite topological defect in numerical cosmology.