Skyrmion formation in 1+1 dimensions with chemical potential

Formation of topological objects during phase transitions has been discussed extensively in literature. In all these discussions defects and anti-defects form with equal probabilities. In contrast, many physical situations, such as formation of baryons in relativistic heavy-ion collisions at present energies, flux tube formation in superconductors in the presence of external magnetic field, and formation of superfluid vortices in a rotating vessel, require a mechanism which can bias (say) defects over anti-defects. Such a bias can crucially affect defect-anti-defect correlations, apart from its effects on defect density. In this paper we initiate an investigation for the basic mechanism of biased formation of defects. For Skyrmions in 1+1 dimensions, we show that incorporation of a chemical potential term in the effective potential leads to a domain structure where order parameter is spatially varying. We show that this leads to biased formation of Skyrmions.