Topological Defects: From Simplicity to Complexity

Abstract

On the one hand simple systems and simple rules can enable surprisingly complex patterns in nature. On the other hand several fundamental questions on natural behavior remain unanswered. For example, dark matter and dark energy have been introduced to explain observed structure and dynamics of the universe. However, their existence is not experimentally supported at fundamental level. It might be that difficulties in understanding of some basic phenomena of the nature arise because we are trying to present it from wrong perspective. There are strong evidences that in physics the fields are fundamental entities of nature and not particles. If this is the case then topological defects (TDs) might play the role of fundamental particles. An adequate testing ground to study and gain fundamental understanding of TDs are nematic liquid crystals. In this paper we present TDs in simple two-dimensional nematics emphasizing their particle-like behavior. We demonstrate strong interactions between TDs and curvature of the space which hosts them. Furthermore, we discuss how using simple rules in a simple system one can predict extremely complex behavior of lattices of TDs.