Thermodynamic and statistical properties of charged topological defects

Abstract
We focus on the statistical and thermodynamic properties of systems with competing long-range interactions. The studies are based on the physics of quasi-one dimensional system with special interest towards their topological defects, the so-called solitons. We have been considering ensembles of solitons resulting from the degeneracy of the ground state of the system. This is the case of various charge density-wave systems such as polyacetylene-like polymers where the solitons are the non-trivial excitations connecting different ground-states. We have been interested in particular with a one component plasma with 3D Coulomb interactions of such defects, mainly in 2 space dimensions. The 3D case has also been considered. The quasi-one dimensional nature of the system is responsible for the confinement of the solitons. This competition between confinement and Coulomb has been formulated and some of its non-trivial effects analyaed. This led us to study the statistical properties of charged interfaces: strings or domain walls in 3D. We have found that shape instabilities, due to the competing interactions, play a fundamental role. The obtained results show similarities with experimental work in the field of stripe phases in cuprate oxides.