  Nematic liquid crystal (LC) is a partially ordered matter that has been a
popular model system for studying a variety of topological behaviors in
condensed matter. In this work, utilizing a spontaneously twisting achiral LC,
we introduce a one-dimensional (1D) model system to investigate how domains and
topological defects arise and annihilate, reminiscing the Kibble-Zurek
mechanism. Because of the unusual elastic properties, lyotropic chromonic LCs
form a double-twist structure in a cylindrical capillary with degenerate planar
anchoring, exhibiting chiral symmetry breaking despite the absence of intrinsic
chirality. Consequently, the domains of different handedness coexist with equal
probabilities, forming the topological defects between them. We experimentally
measure the domain-length distribution and its time evolution, best fitted by a
three-parameter log-normal distribution. We propose that the coalescence within
a train of 1D domains having the normal length distribution and randomly
assigned handedness, may lead to the domains of the log-normal-like length
distribution. Our cylindrically confined LC provides a practical model system
to study the formation and annihilation of domains and defects in 1D.
